Penalized Estimating Functions and Variable Selection in Semiparametric Regression Models

Johnson, Brent A.; Lin, Dahua; Zeng, Donglin

doi:10.1198/016214508000000184

Cited by 145 publications

(141 citation statements)

References 27 publications

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“…Apart from the papers already mentioned, there has been a recent surge of publications establishing the 'oracle' property for a variety of penalized maximum likelihood or related estimators (e.g., Bunea (2004), Bunea & McKeague (2005), Fan & Li (2002, 2004, Li & Liang (2007), Wang & Leng (2007), Wang, G. Li and Jiang (2007), Wang, G. Li and Tsai (2007), Wang, R. Li and Tsai (2007), Yuan & Lin (2007), Zhang & Lu (2007), Zou & Yuan (2008), Zou & Li (2008), Johnson et al (2008)). The 'oracle' property also paints a misleading picture of the behavior of the estimators considered in these papers; see the discussion in Leeb & Pötscher (2005), Yang (2005), Pötscher (2007), Pötscher & Leeb (2007), Leeb & Pötscher (2008b).…”

Section: Introductionmentioning

confidence: 99%

On the distribution of the adaptive LASSO estimator

Pötscher

Schneider

2009

Journal of Statistical Planning and Inference

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We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The largesample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where the tuning results in consistent model selection. We show that the finite-sample as well as the large-sample distributions are typically highly non-normal, regardless of the choice of the tuning parameter. The uniform convergence rate is also obtained, and is shown to be slower than n −1/2 in case the estimator is tuned to perform consistent model selection. In particular, these results question the statistical relevance of the 'oracle' property of the adaptive LASSO estimator established in Zou (2006). Moreover, we also provide an impossibility result regarding the estimation of the distribution function of the adaptive LASSO estimator. The theoretical results, which are obtained for a regression model with orthogonal design, are complemented by a Monte Carlo study using non-orthogonal regressors.MSC 2000 subject classification. Primary 62F11, 62F12, 62E15, 62J05, 62J07.

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Section: Introductionmentioning

confidence: 99%

On the distribution of the adaptive LASSO estimator

Pötscher

Schneider

2009

Journal of Statistical Planning and Inference

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“…As long as is small, the diagonal elements of Σ γ, are very close to those of Σ γ . In fact, this algorithm is identical to that of Hunter and Li (2005) for improvement of a local quadratic approximation (Fan and Li, 2001): Johnson et al (2008). Here, we reportβ = 0 if all five printed decimals are zero.…”

Section: Penalized H-likelihood Proceduresmentioning

confidence: 99%

Variable selection in Poisson HGLMs using h-likelihoood

Ha¹,

Cho²

2015

Journal of the Korean Data and Information Science Society

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Selecting relevant variables for a statistical model is very important in regression analysis. Recently, variable selection methods using a penalized likelihood have been widely studied in various regression models. The main advantage of these methods is that they select important variables and estimate the regression coefficients of the covariates, simultaneously. In this paper, we propose a simple procedure based on a penalized h-likelihood (HL) for variable selection in Poisson hierarchical generalized linear models (HGLMs) for correlated count data. For this we consider three penalty functions (LASSO, SCAD and HL), and derive the corresponding variable-selection procedures. The proposed method is illustrated using a practical example.

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“…To achieve the simultaneous estimation and variable selection, a shrinkage penalty function is developed based on estimating equation with a regularization based shrinkage estimation being defined with the following penalized estimating equation, which is similarly introduced in [17] as…”

Section: Penalized Estimating Equationmentioning

confidence: 99%

“…In this article, the variable selection problem for PLVC model with random effect is investigated. Because of the obvious simplicity and wide usage, a penalized estimating equation based shrinkage estimation procedure is introduced, following the idea of [17].…”

Section: Introductionmentioning

confidence: 99%

Efficient Shrinkage Estimation about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

Li¹

2016

OJS

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In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.

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Penalized Estimating Functions and Variable Selection in Semiparametric Regression Models

Cited by 145 publications

References 27 publications

On the distribution of the adaptive LASSO estimator

On the distribution of the adaptive LASSO estimator

Variable selection in Poisson HGLMs using h-likelihoood

Efficient Shrinkage Estimation about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

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