Página 1 dos resultados de 318 itens digitais encontrados em 0.010 segundos

Multicollinearity and financial constraint in investment decisions: a Bayesian generalized ridge regression

KALATZIS, Aquiles E. G.; BASSETTO, Camila F.; AZZONI, Carlos R.
Fonte: ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD Publicador: ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
66.39%
This paper addresses the investment decisions considering the presence of financial constraints of 373 large Brazilian firms from 1997 to 2004, using panel data. A Bayesian econometric model was used considering ridge regression for multicollinearity problems among the variables in the model. Prior distributions are assumed for the parameters, classifying the model into random or fixed effects. We used a Bayesian approach to estimate the parameters, considering normal and Student t distributions for the error and assumed that the initial values for the lagged dependent variable are not fixed, but generated by a random process. The recursive predictive density criterion was used for model comparisons. Twenty models were tested and the results indicated that multicollinearity does influence the value of the estimated parameters. Controlling for capital intensity, financial constraints are found to be more important for capital-intensive firms, probably due to their lower profitability indexes, higher fixed costs and higher degree of property diversification.; Fundacao de Amparo a Pesquisa do Estado de Sao Paulo - FAPESP

Estimativas de efeitos genotípicos sobre os desempenhos pré e pós-desmama de populações Hereford x Nelore

Cardoso, Vânia; Queiroz, Sandra Aidar de; Fries, Luiz Alberto
Fonte: Sociedade Brasileira de Zootecnia Publicador: Sociedade Brasileira de Zootecnia
Tipo: Artigo de Revista Científica Formato: 1763-1773
Português
Relevância na Pesquisa
46.43%
Objetivou-se obter estimativas de efeitos genéticos aditivos e não-aditivos para as características pré e pós-desmama de animais Hereford x Nelore por meio de análises de regressão linear múltipla, com e sem o uso da técnica de regressão de cumeeira. Avaliaram-se as características ganho médio diário do nascimento à desmama, conformação, precocidade e musculatura à desmama, ganho médio diário da desmama ao sobreano, conformação, precocidade e musculatura ao sobreano e perímetro escrotal ajustado para idade e para idade e peso. Os resultados obtidos sem o uso da técnica indicaram valores acentuados dos fatores de inflação da variância. Para melhor interpretar os efeitos estimados, foram preditos os desempenhos de cinco gerações na formação do Braford ½ em relação à raça Hereford, partindo de vacas da raça Nelore. Os animais da geração F1 apresentaram alto desempenho, em razão do benefício máximo da heterose direta e do efeito aditivo materno. A manifestação completa da epistasia direta reduziu significativamente os desempenhos dos animais da geração F2. Para as características de desmama, os animais da geração F3 mostraram desempenhos menores, em virtude do efeito epistático materno máximo...

Multicollinearity and financial constraint in investment decisions: a bayesian generalized ridge regression

Kalatzis, Aquiles Elie Guimarâes; Azzoni, Carlos Roberto; Bassetto, Camila Fernanda
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Artigo de Revista Científica Formato: 287-299
Português
Relevância na Pesquisa
66.39%
This paper addresses the investment decisions considering the presence of financial constraints of 373 large Brazilian firms from 1997 to 2004, using panel data. A Bayesian econometric model was used considering ridge regression for multicollinearity problems among the variables in the model. Prior distributions are assumed for the parameters, classifying the model into random or fixed effects. We used a Bayesian approach to estimate the parameters, considering normal and Student t distributions for the error and assumed that the initial values for the lagged dependent variable are not fixed, but generated by a random process. The recursive predictive density criterion was used for model comparisons. Twenty models were tested and the results indicated that multicollinearity does influence the value of the estimated parameters. Controlling for capital intensity, financial constraints are found to be more important for capital-intensive firms, probably due to their lower profitability indexes, higher fixed costs and higher degree of property diversification.

Reduced Rank Ridge Regression and Its Kernel Extensions

Mukherjee, Ashin; Zhu, Ji
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.43%
In multivariate linear regression, it is often assumed that the response matrix is intrinsically of lower rank. This could be because of the correlation structure among the prediction variables or the coefficient matrix being lower rank. To accommodate both, we propose a reduced rank ridge regression for multivariate linear regression. Specifically, we combine the ridge penalty with the reduced rank constraint on the coefficient matrix to come up with a computationally straightforward algorithm. Numerical studies indicate that the proposed method consistently outperforms relevant competitors. A novel extension of the proposed method to the reproducing kernel Hilbert space (RKHS) set-up is also developed.

The Stream Algorithm: Computationally Efficient Ridge-Regression via Bayesian Model Averaging, and Applications to Pharmacogenomic Prediction of Cancer Cell Line Sensitivity

Neto, Elias Chaibub; Jang, In Sock; Friend, Stephen H.; Margolin, Adam A.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em //2014 Português
Relevância na Pesquisa
46.59%
Computational efficiency is important for learning algorithms operating in the “large p, small n” setting. In computational biology, the analysis of data sets containing tens of thousands of features (“large p”), but only a few hundred samples (“small n”), is nowadays routine, and regularized regression approaches such as ridge-regression, lasso, and elastic-net are popular choices. In this paper we propose a novel and highly efficient Bayesian inference method for fitting ridge-regression. Our method is fully analytical, and bypasses the need for expensive tuning parameter optimization, via cross-validation, by employing Bayesian model averaging over the grid of tuning parameters. Additional computational efficiency is achieved by adopting the singular value decomposition re-parametrization of the ridge-regression model, replacing computationally expensive inversions of large p × p matrices by efficient inversions of small and diagonal n × n matrices. We show in simulation studies and in the analysis of two large cancer cell line data panels that our algorithm achieves slightly better predictive performance than cross-validated ridge-regression while requiring only a fraction of the computation time. Furthermore, in comparisons based on the cell line data sets...

Heteroscedastic Ridge Regression Approaches for Genome-Wide Prediction With a Focus on Computational Efficiency and Accurate Effect Estimation

Hofheinz, Nina; Frisch, Matthias
Fonte: Genetics Society of America Publicador: Genetics Society of America
Tipo: Artigo de Revista Científica
Publicado em 21/01/2014 Português
Relevância na Pesquisa
46.57%
Ridge regression with heteroscedastic marker variances provides an alternative to Bayesian genome-wide prediction methods. Our objectives were to suggest new methods to determine marker-specific shrinkage factors for heteroscedastic ridge regression and to investigate their properties with respect to computational efficiency and accuracy of estimated effects. We analyzed published data sets of maize, wheat, and sugar beet as well as simulated data with the new methods. Ridge regression with shrinkage factors that were proportional to single-marker analysis of variance estimates of variance components (i.e., RRWA) was the fastest method. It required computation times of less than 1 sec for medium-sized data sets, which have dimensions that are common in plant breeding. A modification of the expectation-maximization algorithm that yields heteroscedastic marker variances (i.e., RMLV) resulted in the most accurate marker effect estimates. It outperformed the homoscedastic ridge regression approach for best linear unbiased prediction in particular for situations with high marker density and strong linkage disequilibrium along the chromosomes, a situation that occurs often in plant breeding populations. We conclude that the RRWA and RMLV approaches provide alternatives to the commonly used Bayesian methods...

Ridge Regression in Prediction Problems: Automatic Choice of the Ridge Parameter

Cule, Erika; De Iorio, Maria
Fonte: BlackWell Publishing Ltd Publicador: BlackWell Publishing Ltd
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.73%
To date, numerous genetic variants have been identified as associated with diverse phenotypic traits. However, identified associations generally explain only a small proportion of trait heritability and the predictive power of models incorporating only known-associated variants has been small. Multiple regression is a popular framework in which to consider the joint effect of many genetic variants simultaneously. Ordinary multiple regression is seldom appropriate in the context of genetic data, due to the high dimensionality of the data and the correlation structure among the predictors. There has been a resurgence of interest in the use of penalised regression techniques to circumvent these difficulties. In this paper, we focus on ridge regression, a penalised regression approach that has been shown to offer good performance in multivariate prediction problems. One challenge in the application of ridge regression is the choice of the ridge parameter that controls the amount of shrinkage of the regression coefficients. We present a method to determine the ridge parameter based on the data, with the aim of good performance in high-dimensional prediction problems. We establish a theoretical justification for our approach, and demonstrate its performance on simulated genetic data and on a real data example. Fitting a ridge regression model to hundreds of thousands to millions of genetic variants simultaneously presents computational challenges. We have developed an R package...

The Current and Future Use of Ridge Regression for Prediction in Quantitative Genetics

de Vlaming, Ronald; Groenen, Patrick J. F.
Fonte: Hindawi Publishing Corporation Publicador: Hindawi Publishing Corporation
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.65%
In recent years, there has been a considerable amount of research on the use of regularization methods for inference and prediction in quantitative genetics. Such research mostly focuses on selection of markers and shrinkage of their effects. In this review paper, the use of ridge regression for prediction in quantitative genetics using single-nucleotide polymorphism data is discussed. In particular, we consider (i) the theoretical foundations of ridge regression, (ii) its link to commonly used methods in animal breeding, (iii) the computational feasibility, and (iv) the scope for constructing prediction models with nonlinear effects (e.g., dominance and epistasis). Based on a simulation study we gauge the current and future potential of ridge regression for prediction of human traits using genome-wide SNP data. We conclude that, for outcomes with a relatively simple genetic architecture, given current sample sizes in most cohorts (i.e., N < 10,000) the predictive accuracy of ridge regression is slightly higher than the classical genome-wide association study approach of repeated simple regression (i.e., one regression per SNP). However, both capture only a small proportion of the heritability. Nevertheless, we find evidence that for large-scale initiatives...

Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions

Shah, Smit
Fonte: FIU Digital Commons Publicador: FIU Digital Commons
Tipo: Artigo de Revista Científica Formato: application/pdf
Português
Relevância na Pesquisa
56.68%
Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

Anomalies in the Foundations of Ridge Regression

Jensen, D. R.; Ramirez, D. E.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/03/2007 Português
Relevância na Pesquisa
46.64%
Anomalies persist in the foundations of ridge regression as set forth in Hoerl and Kennard (1970) and subsequently. Conventional ridge estimators and their properties do not follow on constraining lengths of solution vectors using LaGrange's method, as claimed. Estimators so constrained have singular distributions; the proposed solutions are not necessarily minimizing; and heretofore undiscovered bounds are exhibited for the ridge parameter. None of the considerable literature on estimation, prediction, cross--validation, choice of ridge parameter, and related issues, collectively known as ridge regression, is consistent with constrained optimization, nor with corresponding inequality constraints. The problem is traced to a misapplication of LaGrange's principle, failure to recognize the singularity of distributions, and misplaced links between constraints and the ridge parameter. Other principles, based on condition numbers, are seen to validate both conventional ridge and surrogate ridge regression to be defined. Numerical studies illustrate that ridge analysis often exhibits some of the same pathologies it is intended to redress.

Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates

Zhang, Yuchen; Duchi, John C.; Wainwright, Martin J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.5%
We establish optimal convergence rates for a decomposition-based scalable approach to kernel ridge regression. The method is simple to describe: it randomly partitions a dataset of size N into m subsets of equal size, computes an independent kernel ridge regression estimator for each subset, then averages the local solutions into a global predictor. This partitioning leads to a substantial reduction in computation time versus the standard approach of performing kernel ridge regression on all N samples. Our two main theorems establish that despite the computational speed-up, statistical optimality is retained: as long as m is not too large, the partition-based estimator achieves the statistical minimax rate over all estimators using the set of N samples. As concrete examples, our theory guarantees that the number of processors m may grow nearly linearly for finite-rank kernels and Gaussian kernels and polynomially in N for Sobolev spaces, which in turn allows for substantial reductions in computational cost. We conclude with experiments on both simulated data and a music-prediction task that complement our theoretical results, exhibiting the computational and statistical benefits of our approach.

Fast Marginal Likelihood Estimation of the Ridge Parameter(s) in Ridge Regression and Generalized Ridge Regression for Big Data

Karabatsos, George
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.68%
Unlike the ordinary least-squares (OLS) estimator for the linear model, a ridge regression linear model provides coefficient estimates via shrinkage, usually with improved mean-square and prediction error. This is true especially when the observed design matrix is ill-conditioned or singular, either as a result of highly-correlated covariates or the number of covariates exceeding the sample size. This paper introduces novel and fast marginal maximum likelihood (MML) algorithms for estimating the shrinkage parameter(s) for the Bayesian ridge and power ridge regression models, and an automatic plug-in MML estimator for the Bayesian generalized ridge regression model. With the aid of the singular value decomposition of the observed covariate design matrix, these MML estimation methods are quite fast even for data sets where either the sample size (n) or the number of covariates (p) is very large, and even when p>n. On several real data sets varying widely in terms of n and p, the computation times of the MML estimation methods for the three ridge models, respectively, are compared with the times of other methods for estimating the shrinkage parameter in ridge, LASSO and Elastic Net (EN) models, with the other methods based on minimizing prediction error according to cross-validation or information criteria. Also...

Improving Correlation Function Fitting with Ridge Regression: Application to Cross-Correlation Reconstruction

Matthews, Daniel J.; Newman, Jeffrey A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.57%
Cross-correlation techniques provide a promising avenue for calibrating photometric redshifts and determining redshift distributions using spectroscopy which is systematically incomplete (e.g., current deep spectroscopic surveys fail to obtain secure redshifts for 30-50% or more of the galaxies targeted). In this paper we improve on the redshift distribution reconstruction methods presented in Matthews & Newman (2010) by incorporating full covariance information into our correlation function fits. Correlation function measurements are strongly covariant between angular or spatial bins, and accounting for this in fitting can yield substantial reduction in errors. However, frequently the covariance matrices used in these calculations are determined from a relatively small set (dozens rather than hundreds) of subsamples or mock catalogs, resulting in noisy covariance matrices whose inversion is ill-conditioned and numerically unstable. We present here a method of conditioning the covariance matrix known as ridge regression which results in a more well behaved inversion than other techniques common in large-scale structure studies. We demonstrate that ridge regression significantly improves the determination of correlation function parameters. We then apply these improved techniques to the problem of reconstructing redshift distributions. By incorporating full covariance information...

High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification

Dobriban, Edgar; Wager, Stefan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.5%
We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma \in (0, \, \infty)$, and allow for arbitrary covariance among the features. For both methods, we provide an explicit and efficiently computable expression for the limiting predictive risk, which depends only on the spectrum of the feature-covariance matrix, the signal strength, and the aspect ratio $\gamma$. Especially in the case of regularized discriminant analysis, we find that predictive accuracy has a nuanced dependence on the eigenvalue distribution of the covariance matrix, suggesting that analyses based on the operator norm of the covariance matrix may not be sharp. Our results also uncover several qualitative insights about both methods: for example, with ridge regression, there is an exact inverse relation between the limiting predictive risk and the limiting estimation risk given a fixed signal strength. Our analysis builds on recent advances in random matrix theory.; Comment: Added a section on prediction versus estimation for ridge regression. Rewrote introduction. Other results unchanged

A semi-automatic method to guide the choice of ridge parameter in ridge regression

Cule, Erika; De Iorio, Maria
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/05/2012 Português
Relevância na Pesquisa
46.66%
We consider the application of a popular penalised regression method, Ridge Regression, to data with very high dimensions and many more covariates than observations. Our motivation is the problem of out-of-sample prediction and the setting is high-density genotype data from a genome-wide association or resequencing study. Ridge regression has previously been shown to offer improved performance for prediction when compared with other penalised regression methods. One problem with ridge regression is the choice of an appropriate parameter for controlling the amount of shrinkage of the coefficient estimates. Here we propose a method for choosing the ridge parameter based on controlling the variance of the predicted observations in the model. Using simulated data, we demonstrate that our method outperforms subset selection based on univariate tests of association and another penalised regression method, HyperLasso regression, in terms of improved prediction error. We extend our approach to regression problems when the outcomes are binary (representing cases and controls, as is typically the setting for genome-wide association studies) and demonstrate the method on a real data example consisting of case-control and genotype data on Bipolar Disorder...

Feature Selection for Ridge Regression with Provable Guarantees

Paul, Saurabh; Drineas, Petros
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.5%
We introduce single-set spectral sparsification as a deterministic sampling based feature selection technique for regularized least squares classification, which is the classification analogue to ridge regression. The method is unsupervised and gives worst-case guarantees of the generalization power of the classification function after feature selection with respect to the classification function obtained using all features. We also introduce leverage-score sampling as an unsupervised randomized feature selection method for ridge regression. We provide risk bounds for both single-set spectral sparsification and leverage-score sampling on ridge regression in the fixed design setting and show that the risk in the sampled space is comparable to the risk in the full-feature space. We perform experiments on synthetic and real-world datasets, namely a subset of TechTC-300 datasets, to support our theory. Experimental results indicate that the proposed methods perform better than the existing feature selection methods.; Comment: To appear in Neural Computation. A shorter version of this paper appeared at ECML-PKDD 2014 under the title "Deterministic Feature Selection for Regularized Least Squares Classification."

Lecture notes on ridge regression

van Wieringen, Wessel N.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/09/2015 Português
Relevância na Pesquisa
46.57%
The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a penalty (i.e. a function of regression coefficients). The ridge penalty is the sum of squared regression coefficients, giving rise to ridge regression. Here many aspect of ridge regression are reviewed e.g. moments, mean squared error, its equivalence to constrained estimation, and its relation to Bayesian regression. Finally, its behaviour and use are illustrated in simulation and on omics data.

Adjusted Plus-Minus for NHL Players using Ridge Regression with Goals, Shots, Fenwick, and Corsi

Macdonald, Brian
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.48%
Regression-based adjusted plus-minus statistics were developed in basketball and have recently come to hockey. The purpose of these statistics is to provide an estimate of each player's contribution to his team, independent of the strength of his teammates, the strength of his opponents, and other variables that are out of his control. One of the main downsides of the ordinary least squares regression models is that the estimates have large error bounds. Since certain pairs of teammates play together frequently, collinearity is present in the data and is one reason for the large errors. In hockey, the relative lack of scoring compared to basketball is another reason. To deal with these issues, we use ridge regression, a method that is commonly used in lieu of ordinary least squares regression when collinearity is present in the data. We also create models that use not only goals, but also shots, Fenwick rating (shots plus missed shots), and Corsi rating (shots, missed shots, and blocked shots). One benefit of using these statistics is that there are roughly ten times as many shots as goals, so there is much more data when using these statistics and the resulting estimates have smaller error bounds. The results of our ridge regression models are estimates of the offensive and defensive contributions of forwards and defensemen during even strength...

When Does More Regularization Imply Fewer Degrees of Freedom? Sufficient Conditions and Counter Examples from Lasso and Ridge Regression

Kaufman, Shachar; Rosset, Saharon
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/11/2013 Português
Relevância na Pesquisa
46.46%
Regularization aims to improve prediction performance of a given statistical modeling approach by moving to a second approach which achieves worse training error but is expected to have fewer degrees of freedom, i.e., better agreement between training and prediction error. We show here, however, that this expected behavior does not hold in general. In fact, counter examples are given that show regularization can increase the degrees of freedom in simple situations, including lasso and ridge regression, which are the most common regularization approaches in use. In such situations, the regularization increases both training error and degrees of freedom, and is thus inherently without merit. On the other hand, two important regularization scenarios are described where the expected reduction in degrees of freedom is indeed guaranteed: (a) all symmetric linear smoothers, and (b) linear regression versus convex constrained linear regression (as in the constrained variant of ridge regression and lasso).; Comment: Main text: 15 pages, 2 figures; Supplementary material is included at the end of the main text: 9 pages, 7 figures

On developing ridge regression parameters : a graphical investigation

Muniz, Gisela; Golam Kibria, B. M.; Mansson, Kristofer; Shukur, Ghazi
Fonte: Universidade Autônoma de Barcelona Publicador: Universidade Autônoma de Barcelona
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em //2012 Português
Relevância na Pesquisa
56.32%
In this paper we review some existing and propose some new estimators for estimating the ridge parameter. All in all 19 different estimators have been studied. The investigation has been carried out using Monte Carlo simulations. A large number of different models have been investigated where the variance of the random error, the number of variables included in the model, the correlations among the explanatory variables, the sample size and the unknown coefficient vector were varied. For each model we have performed 2000 replications and presented the results both in term of figures and tables. Based on the simulation study, we found that increasing the number of correlated variable, the variance of the random error and increasing the correlation between the independent variables have negative effect on the mean squared error. When the sample size increases the mean squared error decreases even when the correlation between the independent variables and the variance of the random error are large. In all situations, the proposed estimators have smaller mean squared error than the ordinary least squares and other existing estimators.