Penalized estimation in additive varying coefficient models using grouped regularization

Antoniadis, Anestis; Gijbels, Irène; Lambert-Lacroix, Sophie

doi:10.1007/s00362-013-0522-1

Cited by 14 publications

(12 citation statements)

References 45 publications

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“…for some sufficiently small positive constant C κ3 satisfying C κ3 < C κ2 /2, where C κ2 is given in Assumption M2 (1).…”

Section: 1mentioning

confidence: 99%

“…For longitudinal data, when p is fixed, group SCAD penalized B-spline methods were studied in [29] and [23], and regularized P-spline methods were considered in [2]. When p diverges and p = o(n 2/5 ), where n is the sample size, [32] and [1] examined adaptive group Lasso estimators.…”

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confidence: 99%

“…Under weaker conditions than in the literature, our NIS step can effectively cut the dimensionality down to a moderate order. Writing as x (1) , . .…”

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confidence: 99%

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Nonparametric independence screening and structure identification for ultra-high dimensional longitudinal data

Cheng¹,

Honda²,

Li³

et al. 2014

Ann. Statist.

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Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging both theoretically and methodologically. We offer a new automatic procedure for finding a sparse semivarying coefficient model, which is widely accepted for longitudinal data analysis. Our proposed method first reduces the number of covariates to a moderate order by employing a screening procedure, and then identifies both the varying and constant coefficients using a group SCAD estimator, which is subsequently refined by accounting for the within-subject correlation. The screening procedure is based on working independence and B-spline marginal models. Under weaker conditions than those in the literature, we show that with high probability only irrelevant variables will be screened out, and the number of selected variables can be bounded by a moderate order. This allows the desirable sparsity and oracle properties of the subsequent structure identification step. Note that existing methods require some kind of iterative screening in order to achieve this, thus they demand heavy computational effort and consistency is not guaranteed. The refined semivarying coefficient model employs profile

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“…for some sufficiently small positive constant C κ3 satisfying C κ3 < C κ2 /2, where C κ2 is given in Assumption M2 (1).…”

Section: 1mentioning

confidence: 99%

mentioning

confidence: 99%

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Nonparametric independence screening and structure identification for ultra-high dimensional longitudinal data

Cheng¹,

Honda²,

Li³

et al. 2014

Ann. Statist.

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“…The NNG selection method presented in section NNG Variable Selection is also a grouped regularization method. For recent contributions in grouped regularization methods, see Yuan and Lin, Wang et al, Meier et al, Huang et al, Matsuia and Konishib, Huang et al, Simona et al, Zeng and Xie and Antoniadis et al, among others.…”

Section: P‐splines Variable Selection In Flexible Regression Modelsmentioning

confidence: 99%

Variable selection using P‐splines

Gijbels

Verhasselt

Vrinssen

2014

WIREs Computational Stats

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Selecting among a large set of variables those that influence most a response variable is an important problem in statistics. When the assumed regression model involves a nonparametric component, penalized regression techniques, and in particular P-splines, are among the commonly used methods. The aim of this paper is to provide a brief review of variable selection methods using P-splines. Starting from multiple linear regression models, with least-squares regression, and Ridge regression, we review standard methods that perform variable selection, such as LASSO, nonnegative garrote, the SCAD method, etc. We briefly discuss a general framework of penalization and regularization methods. Going toward more flexible regression models, with some nonparametric component(s), we discuss P-splines estimation. For some examples of flexible regression models, we then review a few variable selection methods using P-splines. A brief discussion on grouped regularization techniques and on a robust variable selection method is given. Furthermore, we mention key ingredients in Bayesian approaches, and end the paper by drawing the attention to several other issues in variable selection with P-splines. Throughout the paper we provide some illustrations. LEAST-SQUARES AND RIDGE REGRESSION In regression analysis the interest is to find out how, on average, a variable of interest Y is influenced by some explanatory variables X 1 , … , X d . In multiple linear regression the relationship between Y and (X 1 , … , X d ) is modeled via T the vector of unknown regression coefficients, and where denotes the error term. The superscript T denotes the transposed of a matrix or a vector.Often measurements on many potential influential factors X 1 , … , X d are available, and selecting among the d variables those that have a significant average influence on the response variable Y, is a major concern.Suppose that an i.i.is available. The ordinary least-squares method consists of solving the optimization problemand results into the least-squares estimatorof . We rewrite the Volume 7, January/February 2015

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“…A model checking or variable selection procedure with such an assumption may not detect significant covariates that have nonlinear effects. Because of this, procedures for both model checking and variable selection have been developed under more general/flexible models; see, for example, Claeskens (2004), Li and Liang (2008), Wang and Xia (2009), Meinshausen, Meier, andBühlmann (2009), Huang, Horowitz, andWei (2010), Storlie, Bondell, Reich, and Zhang (2011), Antoniadis, Gijbels, and Lambert-Lacroix (2014), Gijbels, Verhasselt, and Vrinssen (2015) and references therein. In a completely nonparametric regression, Zambom and Akritas (2014) introduced a variable selection procedure using its conceptual connection with model checking.…”

Section: Introductionmentioning

confidence: 99%

NonpModelCheck: An R Package for Nonparametric Lack-of-Fit Testing and Variable Selection

Zambom

Akritas²

2017

J. Stat. Soft.

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We describe the R package NonpModelCheck for hypothesis testing and variable selection in nonparametric regression. This package implements functions to perform hypothesis testing for the significance of a predictor or a group of predictors in a fully nonparametric heteroscedastic regression model using high-dimensional one-way ANOVA. Based on the p values from the test of each covariate, three different algorithms allow the user to perform variable selection using false discovery rate corrections. A function for classical local polynomial regression is implemented for the multivariate context, where the degree of the polynomial can be as large as needed and bandwidth selection strategies are built in.

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Penalized estimation in additive varying coefficient models using grouped regularization

Cited by 14 publications

References 45 publications

Nonparametric independence screening and structure identification for ultra-high dimensional longitudinal data

Nonparametric independence screening and structure identification for ultra-high dimensional longitudinal data

Variable selection using P‐splines

NonpModelCheck: An R Package for Nonparametric Lack-of-Fit Testing and Variable Selection

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