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Generalized Partially Linear Models With Missing Covariates1

Liang, Hua
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em /05/2008 Português
Relevância na Pesquisa
55.73%
In this article we study a semiparametric generalized partially linear model when the covariates are missing at random. We propose combining local linear regression with the local quasilikelihood technique and weighted estimating equation (WEE) to estimate the parameters and nonparameters when the missing probability is known or unknown. We establish normality of the estimators of the parameter and asymptotic expansion for the estimators of the nonparametric part. We apply the proposed models and methods to a study of the relation between virologic and immunologic responses in AIDS clinical trials, in which virologic response is classified into binary variables. We also give simulation results to illustrate our approach.

Efficient Semiparametric Marginal Estimation for the Partially Linear Additive Model for Longitudinal/Clustered Data

Carroll, Raymond; Maity, Arnab; Mammen, Enno; Yu, Kyusang
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/05/2009 Português
Relevância na Pesquisa
45.87%
We consider the efficient estimation of a regression parameter in a partially linear additive nonparametric regression model from repeated measures data when the covariates are multivariate. To date, while there is some literature in the scalar covariate case, the problem has not been addressed in the multivariate additive model case. Ours represents a first contribution in this direction. As part of this work, we first describe the behavior of nonparametric estimators for additive models with repeated measures when the underlying model is not additive. These results are critical when one considers variants of the basic additive model. We apply them to the partially linear additive repeated-measures model, deriving an explicit consistent estimator of the parametric component; if the errors are in addition Gaussian, the estimator is semiparametric efficient. We also apply our basic methods to a unique testing problem that arises in genetic epidemiology; in combination with a projection argument we develop an efficient and easily computed testing scheme. Simulations and an empirical example from nutritional epidemiology illustrate our methods.

NEW EFFICIENT ESTIMATION AND VARIABLE SELECTION METHODS FOR SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

Kai, Bo; Li, Runze; Zou, Hui
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/02/2011 Português
Relevância na Pesquisa
55.84%
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the semiparametric varying-coefficient partially linear model. We first study quantile regression estimates for the nonparametric varying-coefficient functions and the parametric regression coefficients. To achieve nice efficiency properties, we further develop a semiparametric composite quantile regression procedure. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the estimators achieve the best convergence rate. Moreover, we show that the proposed method is much more efficient than the least-squares-based method for many non-normal errors and that it only loses a small amount of efficiency for normal errors. In addition, it is shown that the loss in efficiency is at most 11.1% for estimating varying coefficient functions and is no greater than 13.6% for estimating parametric components. To achieve sparsity with high-dimensional covariates, we propose adaptive penalization methods for variable selection in the semiparametric varying-coefficient partially linear model and prove that the methods possess the oracle property. Extensive Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures. Finally...

Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models

Zhang, Hao Helen; Cheng, Guang; Liu, Yufeng
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/09/2011 Português
Relevância na Pesquisa
45.96%
Partially linear models provide a useful class of tools for modeling complex data by naturally incorporating a combination of linear and nonlinear effects within one framework. One key question in partially linear models is the choice of model structure, that is, how to decide which covariates are linear and which are nonlinear. This is a fundamental, yet largely unsolved problem for partially linear models. In practice, one often assumes that the model structure is given or known and then makes estimation and inference based on that structure. Alternatively, there are two methods in common use for tackling the problem: hypotheses testing and visual screening based on the marginal fits. Both methods are quite useful in practice but have their drawbacks. First, it is difficult to construct a powerful procedure for testing multiple hypotheses of linear against nonlinear fits. Second, the screening procedure based on the scatterplots of individual covariate fits may provide an educated guess on the regression function form, but the procedure is ad hoc and lacks theoretical justifications. In this article, we propose a new approach to structure selection for partially linear models, called the LAND (Linear And Nonlinear Discoverer). The procedure is developed in an elegant mathematical framework and possesses desired theoretical and computational properties. Under certain regularity conditions...

On the use of partially linear model in identification of arcing-fault location on overhead high-voltage transmission lines

Zivanovic, R.
Fonte: World Scientific Publ Co Pte Ltd Publicador: World Scientific Publ Co Pte Ltd
Tipo: Artigo de Revista Científica
Publicado em //2004 Português
Relevância na Pesquisa
95.88%
The task of locating an arcing-fault on overhead line using sampled measurements obtained at a single line terminal could be classified as a practical nonlinear system identification problem. The practical reasons impose the requirement that the solution should be with maximum possible precision. Dynamic behavior of an arc in open air is influenced by the environmental conditions that are changing randomly, and therefore the useful practically application of parametric modeling is out of question. The requirement to identify only one parameter is yet another specific of this problem. The parameter we need is the one that linearly correlates the voltage samples with the current derivative samples (inductance). The correlation between the voltage samples and the current samples depends on the unpredictable arc dynamic behavior. Therefore this correlation is reconstructed using nonparametric regression. A partially linear model combines both, parametric and nonparametric parts in one model. The fit of this model is noniterative, and provides an efficient way to identify (pull out) a single linear correlation from the nonlinear time series.; Rastko, Zivanovic; © 2004 World Scientific Publishing

Semiparametric penalty function method in partially linear model selection

Dong, C.; Gao, J.; Tong, H.
Fonte: Statistica Sinica Publicador: Statistica Sinica
Tipo: Artigo de Revista Científica
Publicado em //2007 Português
Relevância na Pesquisa
95.9%
Model selection in nonparametric and semiparametric regression is of both theoretical and practical interest. Gao and Tong (2004) proposed a semiparametric leave-more-out cross-validation selection procedure for the choice of both the parametric and nonparametric regressors in a nonlinear time series regression model. As recognized by the authors, the implementation of the proposed procedure requires the availability of relatively large sample sizes. In order to address the model selection problem with small or medium sample sizes, we propose a model selection procedure for practical use. By extending the so-called penalty function method proposed in Zheng and Loh (1995, 1997) through the incorporation of features of the leave-one-out cross-validation approach, we develop a semiparametric, consistent selection procedure suitable for the choice of optimum subsets in a partially linear model. The newly proposed method is implemented using the full set of data, and simulations show that it works well for both small and medium sample sizes.; Chaohua Dong, Jiti Gao and Howell Tong

Semiparametric approximation methods in multivariate model selection

Gao, Jiti; Wolff, Rodney; Anh, Vo
Fonte: Academic Press / Elsevier Publicador: Academic Press / Elsevier
Tipo: Artigo de Revista Científica
Publicado em //2001 Português
Relevância na Pesquisa
55.85%
In this paper we propose a cross-validation selection criterion to determine asymptotically the correct model among the family of all possible partially linear models when the underlying model is a partially linear model. We establish the asymptotic consistency of the criterion. In addition, the criterion is illustrated using two real sets of data.; http://www.elsevier.com/wps/find/journaldescription.cws_home/622865/description#description; Jiti Gao, Rodney Wolff and Vo Anh

Inference on semiparametric models with discrete regressors

Delgado, Miguel A.; Mora, Juan
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /02/1993 Português
Relevância na Pesquisa
55.77%
We study statistical properties of coefficient estimates of the partially linear regression model when some or all regressors, in the unknown part of the model, are discrete. The method does not require smoothing in the discrete variables. Unlike when there are continuous regressors. when all regressors are discrete independence between regressors and regression errors is not required. We also give some guidance on how to implement the estimate when there are both continuous and discrete regressors in the unknown part of the model. Weights employed in this paper seem straightforwardly applicable to other semiparametric problems.

Nonparametric and semiparametric estimation with discrete regressors

Delgado, Miguel A.; Mora, Juan
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /05/1994 Português
Relevância na Pesquisa
55.73%
This paper presents and discusses procedures for estimating regression curves when regressors are discrete and applies them to semiparametric inference problems. We show that pointwise root-n-consistency and global consistency of regression curve estimates are achieved without employing any smoothing, even for discrete regressors with unbounded support. These results still hold when smoothers are used, under much weaker conditions than those required with continuous regressors. Such estimates are useful in semiparametric inference problems. We discuss in detail the partially linear regression model and shape-invariant modelling. We also provide some guidance on estimation in semiparametric models where continuous and discrete regressors are present. The paper also includes a Monte Carlo study.

Statistical inference of nonlinear Granger causality: a semiparametric time series regression analysis.

Lee, Sooyoung
Fonte: Universidade de Adelaide Publicador: Universidade de Adelaide
Tipo: Tese de Doutorado
Publicado em //2013 Português
Relevância na Pesquisa
55.94%
Since the seminal work of Granger (1969), Granger causality has become a useful concept and tool in the study of the dynamic linkages between economic variables and to explore whether or not an economic variable helps forecast another one. Researchers have suggested a variety of methods to test the existence of Grangercausality in the literature. In particular, linear Granger causality testing has been remarkably developed; (see, for example, Toda & Philips (1993), Sims, Stock & Watson (1990), Geweke (1982), Hosoya (1991) and Hidalgo (2000)). However, in practice, the real economic relationship between different variables may often be nonlinear. Hiemstra & Jones (1994) and Nishiyama, Hitomi, Kawasaki & Jeong (2011) recently proposed different methods to test the existence of any non-linear Granger causality between a pair of economic variables under a α-mixing framework of data generating process. Their methods are general with nonparametric features, which however suffer from curse of dimensionality when high lag orders need to be taken into consideration in applications. In this thesis, the main objective is to develop a class of semiparametric time series regression models that are of partially linear structures, with statistical theory established under a more general framework of near epoch dependent (NED) data generating processes...

Generalized Partially Linear Models for Incomplete Longitudinal Data In the Presence of Population-Level Information

Chen, Baojiang; Zhou, Xiao-Hua
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
55.69%
In observational studies, interest often lies in estimation of the population-level relationship between the explanatory variables and dependent variables, and the estimation is often done using longitudinal data. Longitudinal data often feature sampling error and bias due to non-random drop-out. However, inclusion of population-level information can increase estimation efficiency. In this paper we consider a generalized partially linear model for incomplete longitudinal data in the presence of the population-level information. A pseudo-empirical likelihood-based method is introduced to incorporate population-level information, and non-random drop-out bias is corrected by using a weighted generalized estimating equations method. A three-step estimation procedure is proposed, which makes the computation easier. Several methods that are often used in practice are compared in simulation studies, which demonstrate that our proposed method can correct the non-random drop-out bias and increase the estimation efficiency, especially for small sample size or when the missing proportion is high. We apply this method to an Alzheimer's disease study.

Estimación robusta en modelos parcialmente lineales generalizados; Robust estimation in generalized partially linear models

Rodríguez, Daniela A.
Fonte: Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires Publicador: Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires
Tipo: info:eu-repo/semantics/doctoralThesis; tesis doctoral; info:eu-repo/semantics/publishedVersion Formato: application/pdf
Publicado em //2007 Português
Relevância na Pesquisa
65.84%
En esta tesis, introducimos una nueva clase de estimadores robustos para las componentes paramétricas y noparamétricas bajo dos modelos parcialmente lineales generalizados. En el primero, las observaciones independientes (yi, xi, ti), 1 = i = n satisfacen yi| (xi, ti) ~ F (·, µi) con µi = H (n(ti) + xti ß), para una función de distribución F y una función de vínculo H conocidas, donde ti e IR, xi e IR^p. La función n : IR --IR y el parámetro ß son las cantidades a estimar. Los estimadores robustos se basan en un procedimiento en dos pasos en el que valores grandes de la deviance o de los residuos de Pearson se controlan a través de una función de escores acotada. Los estimadores robustos de ß resultan ser n^1/2-consistentes y asintóticamente normales. El comportamiento de estos estimadores se compara con el de los estimadores clásicamente usados, a través de un estudio de Monte Carlo. Por otra parte, la función de influencia empírica permite estudiar la sensibilidad de los estimadores. El modelo generalizado parcialmente lineal de índice simple, generaliza el anterior pues las observaciones independientes son tales que yi| (xi, ti) ~ F (·, µi) con µi = H (n(a tti) + xtiß), donde ahora ti e IR^q, xi e IR^p y la función ß : IR -- IR y los parámetros ß y a (|| a|| =1) son desconocidos y se desean estimar. Introducimos dos familias de estimadores robustos que resultan ser consistentes y asintóticamente normales. Calculamos también su función de influencia empírica. Todas las propuestas dadas mejoran el comportamiento de los estimadores clásicos en presencia de observaciones atípicas.; In this thesis...

Estimating and forecasting partially linear models with non stationary exogeneous variables

Brossat, Xavier; Oppenheim, Georges; Viano, Marie-Claude
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/02/2011 Português
Relevância na Pesquisa
55.69%
This paper presents a backfitting-type method for estimating and forecasting a periodically correlated partially linear model with exogeneous variables and heteroskedastic input noise. A rate of convergence of the estimator is given. The results are valid even if the period is unknown.

Fused kernel-spline smoothing for repeatedly measured outcomes in a generalized partially linear model with functional single index

Jiang, Fei; Ma, Yanyuan; Wang, Yuanjia
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/10/2015 Português
Relevância na Pesquisa
55.77%
We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and modify the generalized estimating equation to facilitate estimation and inference. We use local smoothing kernel to estimate the unspecified coefficient functions of time, and use B-splines to estimate the unspecified function of the single index component. The covariance structure is taken into account via a working model, which provides valid estimation and inference procedure whether or not it captures the true covariance. The estimation method is applicable to both continuous and discrete outcomes. We derive large sample properties of the estimation procedure and show a different convergence rate for each component of the model. The asymptotic properties when the kernel and regression spline methods are combined in a nested fashion has not been studied prior to this work, even in the independent data case.; Comment: Published at http://dx.doi.org/10.1214/15-AOS1330 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

New efficient estimation and variable selection methods for semiparametric varying-coefficient partially linear models

Kai, Bo; Li, Runze; Zou, Hui
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 08/03/2011 Português
Relevância na Pesquisa
55.84%
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the semiparametric varying-coefficient partially linear model. We first study quantile regression estimates for the nonparametric varying-coefficient functions and the parametric regression coefficients. To achieve nice efficiency properties, we further develop a semiparametric composite quantile regression procedure. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the estimators achieve the best convergence rate. Moreover, we show that the proposed method is much more efficient than the least-squares-based method for many non-normal errors and that it only loses a small amount of efficiency for normal errors. In addition, it is shown that the loss in efficiency is at most 11.1% for estimating varying coefficient functions and is no greater than 13.6% for estimating parametric components. To achieve sparsity with high-dimensional covariates, we propose adaptive penalization methods for variable selection in the semiparametric varying-coefficient partially linear model and prove that the methods possess the oracle property. Extensive Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures. Finally...

Robust estimates in generalized partially linear models

Boente, Graciela; He, Xuming; Zhou, Jianhui
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/08/2007 Português
Relevância na Pesquisa
55.69%
In this paper, we introduce a family of robust estimates for the parametric and nonparametric components under a generalized partially linear model, where the data are modeled by $y_i|(\mathbf{x}_i,t_i)\sim F(\cdot,\mu_i)$ with $\mu_i=H(\eta(t_i)+\mathbf{x}_i^{$\mathrm{T}$}\beta)$, for some known distribution function F and link function H. It is shown that the estimates of $\beta$ are root-n consistent and asymptotically normal. Through a Monte Carlo study, the performance of these estimators is compared with that of the classical ones.; Comment: Published at http://dx.doi.org/10.1214/009053606000000858 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Estimation of Partially Linear Regression Model under Partial Consistency Property

Cui, Xia; Lu, Ying; Peng, Heng
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/01/2014 Português
Relevância na Pesquisa
55.87%
In this paper, utilizing recent theoretical results in high dimensional statistical modeling, we propose a model-free yet computationally simple approach to estimate the partially linear model $Y=X\beta+g(Z)+\varepsilon$. Motivated by the partial consistency phenomena, we propose to model $g(Z)$ via incidental parameters. Based on partitioning the support of $Z$, a simple local average is used to estimate the response surface. The proposed method seeks to strike a balance between computation burden and efficiency of the estimators while minimizing model bias. Computationally this approach only involves least squares. We show that given the inconsistent estimator of $g(Z)$, a root $n$ consistent estimator of parametric component $\beta$ of the partially linear model can be obtained with little cost in efficiency. Moreover, conditional on the $\beta$ estimates, an optimal estimator of $g(Z)$ can then be obtained using classic nonparametric methods. The statistical inference problem regarding $\beta$ and a two-population nonparametric testing problem regarding $g(Z)$ are considered. Our results show that the behavior of test statistics are satisfactory. To assess the performance of our method in comparison with other methods, three simulation studies are conducted and a real dataset about risk factors of birth weights is analyzed.

Sparse Partially Linear Additive Models

Lou, Yin; Bien, Jacob; Caruana, Rich; Gehrke, Johannes
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/07/2014 Português
Relevância na Pesquisa
45.9%
The generalized partially linear additive model (GPLAM) is a flexible and interpretable approach to building predictive models. It combines features in an additive manner, allowing them to have either a linear or nonlinear effect on the response. However, the assignment of features to the linear and nonlinear groups is typically assumed known. Thus, to make a GPLAM a viable approach in situations in which little is known $apriori$ about the features, one must overcome two primary model selection challenges: deciding which features to include in the model and determining which features to treat nonlinearly. We introduce sparse partially linear additive models (SPLAMs), which combine model fitting and $both$ of these model selection challenges into a single convex optimization problem. SPLAM provides a bridge between the Lasso and sparse additive models. Through a statistical oracle inequality and thorough simulation, we demonstrate that SPLAM can outperform other methods across a broad spectrum of statistical regimes, including the high-dimensional ($p\gg N$) setting. We develop efficient algorithms that are applied to real data sets with half a million samples and over 45,000 features with excellent predictive performance.

Alternative Asymptotics and the Partially Linear Model with Many Regressors

Cattaneo, Matias D.; Jansson, Michael; Newey, Whitney K.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/05/2015 Português
Relevância na Pesquisa
65.73%
Non-standard distributional approximations have received considerable attention in recent years. They often provide more accurate approximations in small samples, and theoretical improvements in some cases. This paper shows that the seemingly unrelated "many instruments asymptotics" and "small bandwidth asymptotics" share a common structure, where the object determining the limiting distribution is a V-statistic with a remainder that is an asymptotically normal degenerate U-statistic. We illustrate how this general structure can be used to derive new results by obtaining a new asymptotic distribution of a series estimator of the partially linear model when the number of terms in the series approximation possibly grows as fast as the sample size, which we call "many terms asymptotics".

Component Identification and Estimation in Nonlinear High-Dimensional Regression Models by Structural Adaptation

Samarov, Alexander; Spokoiny, Vladimir; Vial, Celine
Fonte: American Statistical Association Publicador: American Statistical Association
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
65.92%
This article proposes a new method of analysis of a partially linear model whose nonlinear component is completely unknown. The target of analysis is identification of the set of regressors that enter in a nonlinear way in the model function, and complete estimation of the model, including slope coefficients of the linear component and the link function of the nonlinear component The procedure also allows selection of the significant regression variables. We also develop a test of linear hypothesis against a partially linear alternative or, more generally, a test that the nonlinear component is M-dimensional for M = 0,1,2,.... The approach proposed in this article is fully adaptive to the unknown model structure and applies under mild conditions on the model. The only important assumption is that the dimensionality of nonlinear component is relatively small. The theoretical results indicate that the procedure provides a prescribed level of the identification error and estimates the linear component with accuracy of order n -1/2. A numerical study demonstrates a very good performance of the method for even small or moderate sample sizes.