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"Regressão beta"; Beta regression

Ospina, Patricia Leone Espinheira
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 29/03/2007 Português
Relevância na Pesquisa
26.37%
Muitos estudos em diferentes áreas examinam como um conjunto de variáveis influencia algum tipo de percentagem, proporção ou frações. Modelos de regressão lineares não são satisfatórios para modelar tais dados. Uma classe de modelos de regressão beta que em muitos aspectos é semelhante aos modelos lineares generalizados foi proposto por Ferrari e Cribari--Neto~(2004). A resposta média é relacionada com um predictor linear por uma função de ligação e o predictor linear envolve covariáveis e parâmetros de regressão desconhecidos. O modelo também é indexado por um parâmetro de precisão. Smithson e Verkuilen,(2005), entre outros, consideram o modelo de regressão beta em que esse parâmetro varia ao longo das observações. Nesta tese foram desenvolvidas técnicas de diagnóstico para os modelos regressão beta com dispersão constante e com dispersão variável, sendo que o método e influência local (Cook,~1986) mostrou-se decisivo, inclusive no sentido de identificar dispersão variável nos dados. Adicionalmente, avaliamos através de estudos de simulação o desempenho de estimadores de máxima verossimilhança para o modelo de regressão beta com dispersão variável, as conseqüências de estimar o modelo supondo dispersão constante quando de fato ela é variável e de testes assintóticos para testar a hipótese de dispersão constante. Finalmente...

Escore clínico-patológico para predizer o risco de metástases e recorrência local em pacientes com carcinoma cortical adrenal e papel do algoritmo da reticulina na distinção entre adenomas e carcinomas corticais adrenais; Clinicopathological score for predicting the risk of metastases and local recurrence in patients with adrenal cortical carcinoma and role of the reticulin algorithm in distinguishing between adrenal cortical adenomas and carcinomas

Freire, Daniel Soares
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 05/05/2014 Português
Relevância na Pesquisa
26.25%
INTRODUÇÃO: o padrão-ouro para o diagnóstico histológico dos tumores corticais adrenais (TCAs) e sua diferenciação entre adenomas e carcinomas é o sistema de Weiss, cuja aplicação é limitada pela baixa reprodutibilidade de alguns dos critérios que o compõe. Recentemente foi proposto e validado um algoritmo diagnóstico para os TCAs baseado na integridade do arcabouço de reticulina e da membrana basal. Os carcinomas adrenais são tumores raros e apresentam prognóstico reservado, mesmo nos pacientes com doença aparentemente localizada. Além do estadiamento e da extensão da ressecção cirúrgica, outros dados foram reportados na literatura como tendo importância prognóstica, tais como idade ao diagnóstico, padrão funcional, tamanho tumoral, extensão local do tumor primário e alguns achados histológicos e imuno-histoquímicos, com destaque à taxa mitótica e ao índice de Ki-67. O sistema de Weiss, embora permita o diagnóstico diferencial entre adenomas e carcinomas, não foi testado completamente como uma ferramenta para distinguir os carcinomas com boa evolução clínica daqueles com desfecho desfavorável. OBJETIVOS: o presente estudo teve como objetivo primário construir um nomograma para estimar o risco de metástases e recorrência local em portadores de carcinoma adrenal...

Bootstrapping high frequency data

Hounyo, Koomla Ulrich
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation
Português
Relevância na Pesquisa
26.66%
Nous développons dans cette thèse, des méthodes de bootstrap pour les données financières de hautes fréquences. Les deux premiers essais focalisent sur les méthodes de bootstrap appliquées à l’approche de "pré-moyennement" et robustes à la présence d’erreurs de microstructure. Le "pré-moyennement" permet de réduire l’influence de l’effet de microstructure avant d’appliquer la volatilité réalisée. En se basant sur cette ap- proche d’estimation de la volatilité intégrée en présence d’erreurs de microstructure, nous développons plusieurs méthodes de bootstrap qui préservent la structure de dépendance et l’hétérogénéité dans la moyenne des données originelles. Le troisième essai développe une méthode de bootstrap sous l’hypothèse de Gaussianité locale des données financières de hautes fréquences. Le premier chapitre est intitulé: "Bootstrap inference for pre-averaged realized volatility based on non-overlapping returns". Nous proposons dans ce chapitre, des méthodes de bootstrap robustes à la présence d’erreurs de microstructure. Particulièrement nous nous sommes focalisés sur la volatilité réalisée utilisant des rendements "pré-moyennés" proposés par Podolskij et Vetter (2009)...

Nonparametric Testing Methods for Treatment-Biomarker Interaction based on Local Partial-Likelihood

Liu, Yicong
Fonte: Quens University Publicador: Quens University
Tipo: Relatório
Português
Relevância na Pesquisa
36.3%
A fair amount of research has been done on the interactions between treatment and biomarkers hoping to avoid failure to recognize effective agents which benefit only a subset of patients in traditional clinical designs and analysis, such as (Bonetti, 2004), (Bonetti et al., 2009), and (Royston and Sauerbrei, 2004). Particularly, Fan et al. (Fan et al., 2006) assumed the treatment effect is an unknown function of a putative biomarker, and proposed techniques to give the local partial likelihood estimation (LPLE) of this treatment effect function using local linear techniques (Fan and Chen, 1999). However, no methods were developed for assessing whether the treatment effect is indeed a function of the biomarker (interaction exists) or just a constant (no interactions). Based on the idea of LPLE, a new nonparametric hypothesis testing methodology, which we call local partial likelihood bootstrap (LPLB) test, is proposed in this work to identify the differences in treatment effects among subgroups of patients with different values of biomarkers in a Phase III clinical trials study. A bootstrap technique is used to evaluate the significance of the test. Meanwhile, the proposed method can also be applied to identify the interactions between a putative biomarker and a collection of covariates (covariate vectors) that are discrete or continuous. Numerical studies show that the LPLB test can provide a substantial improvement in the power of the interaction detection compared with the commonly used method...

Assessing extrema of empirical principal component functions

Hall, Peter; Vial, Céline
Fonte: Institute of Mathematical Statistics Publicador: Institute of Mathematical Statistics
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.27%
The difficulties of estimating and representing the distributions of functional data mean that principal component methods play a substantially greater role in functional data analysis than in more conventional finite-dimensional settings. Local maxima and minima in principal component functions are of direct importance; they indicate places in the domain of a random function where influence on the function value tends to be relatively strong but of opposite sign. We explore statistical properties of the relationship between extrema of empirical principal component functions, and their counterparts for the true principal component functions. It is shown that empirical principal component funcions have relatively little trouble capturing conventional extrema, but can experience difficulty distinguishing a ``shoulder' in a curve from a small bump. For example, when the true principal component function has a shoulder, the probability that the empirical principal component function has instead a bump is approximately equal to 1/2. We suggest and describe the performance of bootstrap methods for assessing the strength of extrema. It is shown that the subsample bootstrap is more effective than the standard bootstrap in this regard. A ``bootstrap likelihood' is proposed for measuring extremum strength. Exploratory numerical methods are suggested.

Bootstrap prediction intervals in State Space models

Rodríguez, Alejandro; Ruiz, Esther
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /03/2008 Português
Relevância na Pesquisa
36.34%
Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally...

Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Rodríguez, Alejandro; Ruiz, Esther
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /01/2010 Português
Relevância na Pesquisa
26.24%
Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally...

Nonparametric estimation and inference for Granger causality measures

Taamouti, Abderrahim; Bouezmarni, Taoufik; El Ghouch, Anouar
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper Formato: application/pdf
Publicado em 29/03/2012 Português
Relevância na Pesquisa
36.29%
We propose a nonparametric estimator and a nonparametric test for Granger causality measures that quantify linear and nonlinear Granger causality in distribution between random variables. We first show how to write the Granger causality measures in terms of copula densities. We suggest a consistent estimator for these causality measures based on nonparametric estimators of copula densities. Further, we prove that the nonparametric estimators are asymptotically normally distributed and we discuss the validity of a local smoothed bootstrap that we use in finite sample settings to compute a bootstrap bias-corrected estimator and test for our causality measures. A simulation study reveals that the bias-corrected bootstrap estimator of causality measures behaves well and the corresponding test has quite good finite sample size and power properties for a variety of typical data generating processes and different sample sizes. Finally, we illustrate the practical relevance of nonparametric causality measures by quantifying the Granger causality between S&P500 Index returns and many exchange rates (US/Canada, US/UK and US/Japen exchange rates).

Bootstrap prediction intervals in state space models

Rodríguez, Alejandro; Ruiz, Esther
Fonte: Wiley-Blackwell Publicador: Wiley-Blackwell
Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article Formato: application/pdf
Publicado em //2009 Português
Relevância na Pesquisa
36.29%
Prediction intervals in state space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, with the true parameters substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty caused by parameter estimation. Second, the Gaussianity of future innovations assumption may be inaccurate. To overcome these drawbacks, Wall and Stoffer [Journal of Time Series Analysis (2002) Vol. 23, pp. 733 751] propose a bootstrap procedure for evaluating conditional forecast errors that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. In this article, we propose a bootstrap procedure for constructing prediction intervals directly for the observations, which does not need the backward representation of the model. Consequently, its application is much simpler, without losing the good behaviour of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer procedures for the local level model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series.; Financial support from Project SEJ2006-03919 by the Spanish Government is gratefully acknowledged

Local Bootstrap Percolation

Gravner, Janko; Holroyd, Alexander E.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/06/2008 Português
Relevância na Pesquisa
36.02%
We study a variant of bootstrap percolation in which growth is restricted to a single active cluster. Initially there is a single active site at the origin, while other sites of Z^2 are independently occupied with small probability p, otherwise empty. Subsequently, an empty site becomes active by contact with 2 or more active neighbors, and an occupied site becomes active if it has an active site within distance 2. We prove that the entire lattice becomes active with probability exp[alpha(p)/p], where alpha(p) is between -pi^2/9 + c sqrt p and pi^2/9 + C sqrt p (-log p)^3. This corrects previous numerical predictions for the scaling of the correction term.; Comment: 19 pages, 2 figures

Form factors in finite volume I: form factor bootstrap and truncated conformal space

Pozsgay, B.; Takacs, G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.29%
We describe the volume dependence of matrix elements of local fields to all orders in inverse powers of the volume (i.e. only neglecting contributions that decay exponentially with volume). Using the scaling Lee-Yang model and the Ising model in a magnetic field as testing ground, we compare them to matrix elements extracted in finite volume using truncated conformal space approach to exact form factors obtained using the bootstrap method. We obtain solid confirmation for the form factor bootstrap, which is different from all previously available tests in that it is a non-perturbative and direct comparison of exact form factors to multi-particle matrix elements of local operators, computed from the Hamiltonian formulation of the quantum field theory. We also demonstrate that combining form factor bootstrap and truncated conformal space is an effective method for evaluating finite volume form factors in integrable field theories over the whole range in volume.; Comment: 43 pages, 31 eps figures, LaTeX2e file. v2: main theoretical argument substantially expanded and clarified, typos and references corrected

Local and global Fokker-Planck neoclassical calculations showing flow and bootstrap current modification in a pedestal

Landreman, Matt; Ernst, Darin R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.34%
In transport barriers, particularly H-mode edge pedestals, radial scale lengths can become comparable to the ion orbit width, causing neoclassical physics to become radially nonlocal. In this work, the resulting changes to neoclassical flow and current are examined both analytically and numerically. Steep density gradients are considered, with scale lengths comparable to the poloidal ion gyroradius, together with strong radial electric fields sufficient to electrostatically confine the ions. Attention is restricted to relatively weak ion temperature gradients (but permitting arbitrary electron temperature gradients), since in this limit a delta-f (small departures from a Maxwellian distribution) rather than full-f approach is justified. This assumption is in fact consistent with measured inter-ELM H-Mode edge pedestal density and ion temperature profiles in many present experiments, and is expected to be increasingly valid in future lower collisionality experiments. In the numerical analysis, the distribution function and Rosenbluth potentials are solved for simultaneously, allowing use of the exact field term in the linearized Fokker-Planck collision operator. In the pedestal, the parallel and poloidal flows are found to deviate strongly from the best available conventional neoclassical prediction...

Bootstrap kernel for organic low dimensional systems; PPV, pentacene and picene

Sharma, S.; Dewhurst, J. K.; Gross, E. K. U.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 08/11/2013 Português
Relevância na Pesquisa
26.29%
We apply the bootstrap kernel within time dependent density functional theory to study one-dimensional chain of organic polymer poly-phenylene-vinylene and molecular crystals of picene and pentacene. The behaviour of this kernel in the presence and absence of local field effects is studied. The absorption spectra of poly-phenylene-vinylene has a bound excitonic peak which is well reproduced by the bootstrap kernel. Pentacene and picene, electronically similar materials, have remarkably different excitonic physics which is also captured properly by the bootstrap kernel. Inclusion of local-field effects dramatically change the spectra for both picene and pentacene. We highlight the reason behind this change. This also sheds light on the reasons behind the discrepancy in results between two different previous Bethe-Salpeter calculations.; Comment: 5 figs

Subcritical $\mathcal{U}$-bootstrap percolation models have non-trivial phase transitions

Balister, Paul; Bollobás, Béla; Przykucki, Michał; Smith, Paul
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.37%
We prove that there exist natural generalizations of the classical bootstrap percolation model on $\mathbb{Z}^2$ that have non-trivial critical probabilities, and moreover we characterize all homogeneous, local, monotone models with this property. Van Enter (in the case $d=r=2$) and Schonmann (for all $d \geq r \geq 2$) proved that $r$-neighbour bootstrap percolation models have trivial critical probabilities on $\mathbb{Z}^d$ for every choice of the parameters $d \geq r \geq 2$: that is, an initial set of density $p$ almost surely percolates $\mathbb{Z}^d$ for every $p>0$. These results effectively ended the study of bootstrap percolation on infinite lattices. Recently Bollob\'as, Smith and Uzzell introduced a broad class of percolation models called $\mathcal{U}$-bootstrap percolation, which includes $r$-neighbour bootstrap percolation as a special case. They divided two-dimensional $\mathcal{U}$-bootstrap percolation models into three classes -- subcritical, critical and supercritical -- and they proved that, like classical 2-neighbour bootstrap percolation, critical and supercritical $\mathcal{U}$-bootstrap percolation models have trivial critical probabilities on $\mathbb{Z}^2$. They left open the question as to what happens in the case of subcritical families. In this paper we answer that question: we show that every subcritical $\mathcal{U}$-bootstrap percolation model has a non-trivial critical probability on $\mathbb{Z}^2$. This is new except for a certain `degenerate' subclass of symmetric models that can be coupled from below with oriented site percolation. Our results re-open the study of critical probabilities in bootstrap percolation on infinite lattices...

Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap

Poskitt, D. S.; Martin, Gael M.; Grose, Simone D.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/02/2014 Português
Relevância na Pesquisa
26.3%
This paper investigates the use of bootstrap-based bias correction of semi-parametric estimators of the long memory parameter in fractionally integrated processes. The re-sampling method involves the application of the sieve bootstrap to data pre-filtered by a preliminary semi-parametric estimate of the long memory parameter. Theoretical justification for using the bootstrap techniques to bias adjust log-periodogram and semi-parametric local Whittle estimators of the memory parameter is provided. Simulation evidence comparing the performance of the bootstrap bias correction with analytical bias correction techniques is also presented. The bootstrap method is shown to produce notable bias reductions, in particular when applied to an estimator for which analytical adjustments have already been used. The empirical coverage of confidence intervals based on the bias-adjusted estimators is very close to the nominal, for a reasonably large sample size, more so than for the comparable analytically adjusted estimators. The precision of inferences (as measured by interval length) is also greater when the bootstrap is used to bias correct rather than analytical adjustments.; Comment: 38 pages

Simultaneous likelihood-based bootstrap confidence sets for a large number of models

Zhilova, Mayya
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/06/2015 Português
Relevância na Pesquisa
26.34%
The paper studies a problem of constructing simultaneous likelihood-based confidence sets. We consider a simultaneous multiplier bootstrap procedure for estimating the quantiles of the joint distribution of the likelihood ratio statistics, and for adjusting the confidence level for multiplicity. Theoretical results state the bootstrap validity in the following setting: the sample size \(n\) is fixed, the maximal parameter dimension \(p_{\textrm{max}}\) and the number of considered parametric models \(K\) are s.t. \((\log K)^{12}p_{\max}^{3}/n\) is small. We also consider the situation when the parametric models are misspecified. If the models' misspecification is significant, then the bootstrap critical values exceed the true ones and the simultaneous bootstrap confidence set becomes conservative. Numerical experiments for local constant and local quadratic regressions illustrate the theoretical results.

Biased bootstrap methods for reducing the effects of contamination

Hall, Peter; Presnell, B
Fonte: Aiden Press Publicador: Aiden Press
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
36.19%
Contamination of a sampled distribution, for example by a heavy-tailed distribution, can degrade the performance of a statistical estimator. We suggest a general approach to alleviating this problem, using a version of the weighted bootstrap. The idea is

Intentionally biased bootstrap methods

Hall, Peter; Presnell, B
Fonte: Aiden Press Publicador: Aiden Press
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
36.44%
A class of weighted bootstrap techniques, called biased bootstrap or b-bootstrap methods, is introduced. It is motivated by the need to adjust empirical methods, such as the "uniform" bootstrap, in a surgical way to alter some of their features while leaving others unchanged. Depending on the nature of the adjustment, the b-bootstrap can be used to reduce bias, or to reduce variance or to render some characteristic equal to a predetermined quantity. Examples of the last application include a b-bootstrap approach to hypothesis testing in nonparametric contexts, where the b-bootstrap enables simulation "under the null hypothesis", even when the hypothesis is false, and a b-bootstrap competitor to Tibshirani's variance stabilization method. An example of the bias reduction application is adjustment of Nadaraya-Watson kernel estimators to make them competitive with local linear smoothing. Other applications include density estimation under constraints, outlier trimming, sensitivity analysis, skewness or kurtosis reduction and shrinkage.

Reducing bias in curve estimation by use of weights

Hall, Peter; Turlach, B
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.27%
A technique is suggested for reducing the order of bias of kernel estimators by weighting the contributions that different data values make to the estimator. The method is developed initially in the context of density estimation, where, unlike the 'variable kernel' method proposed by Abramson, our approach does not involve using different bandwidths at different data values. Rather, it is a weighted-bootstrap version of the standard uniform-bootstrap method that is used to construct traditional kernel density estimators. The reduction in bias is achieved by biasing the bootstrap appropriately, in a global rather than local way. Our technique has a variety of different forms, each of which reduces the order of bias from the square to the fourth power of bandwidth, but does not alter the order of variance. It has immediate application to nonparametric regression, where it allows bias to be reduced without prejudicing the one sign of an estimator.

Bandwidth choice for local polynomial estimation of smooth boundaries

Hall, Peter; Park, B
Fonte: Academic Press Publicador: Academic Press
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
36.04%
Local polynomial methods hold considerable promise for boundary estimation, where they offer unmatched flexibility and adaptivity. Most rival techniques provide only a single order of approximation; local polynomial approaches allow any order desired. Their more conventional rivals, for example high-order kernel methods in the context of regression, do not have attractive versions in the case of boundary estimation. However, the adoption of local polynomial methods for boundary estimation is inhibited by lack of knowledge about their properties, in particular about the manner in which they are influenced by bandwidth; and by the absence of techniques for empirical bandwidth choice. In the present paper we detail the way in which bandwidth selection determines mean squared error of local polynomial boundary estimators, showing that it is substantially more complex than in regression settings. For example, asymptotic formulae for bias and variance contributions to mean squared error no longer decompose into monotone functions of bandwidth. Nevertheless, once these properties are understood, relatively simple empirical bandwidth selection methods can be developed. We suggest a new approach to both local and global bandwidth choice, and describe its properties.