scholarly journals Asymptotic Normality of Posterior Distributions in High-Dimensional Linear Models

Bernoulli ◽  
1999 ◽  
Vol 5 (2) ◽  
pp. 315 ◽  
Author(s):  
Subhashis Ghosal
Keyword(s):  
Asymptotic Normality ◽  
Linear Models ◽  
High Dimensional ◽  
Posterior Distributions

scholarly journals GENERALIZED ADDITIVE PARTIAL LINEAR MODELS WITH HIGH-DIMENSIONAL COVARIATES

2013 ◽  
Vol 29 (6) ◽  
pp. 1136-1161 ◽  
Author(s):  
Heng Lian ◽  
Hua Liang
Keyword(s):  
Monte Carlo ◽  
Asymptotic Normality ◽  
Linear Models ◽  
High Dimensional ◽  
Initial Estimate ◽  
Polynomial Splines ◽  
Partial Linear ◽  
Selection Operator ◽  
Partial Linear Models ◽  
Final Selection

This paper studies generalized additive partial linear models with high-dimensional covariates. We are interested in which components (including parametric and nonparametric components) are nonzero. The additive nonparametric functions are approximated by polynomial splines. We propose a doubly penalized procedure to obtain an initial estimate and then use the adaptive least absolute shrinkage and selection operator to identify nonzero components and to obtain the final selection and estimation results. We establish selection and estimation consistency of the estimator in addition to asymptotic normality for the estimator of the parametric components by employing a penalized quasi-likelihood. Thus our estimator is shown to have an asymptotic oracle property. Monte Carlo simulations show that the proposed procedure works well with moderate sample sizes.

scholarly journals Drawing inferences for high‐dimensional linear models: A selection‐assisted partial regression and smoothing approach

Biometrics ◽  
2019 ◽  
Vol 75 (2) ◽  
pp. 551-561
Author(s):  
Zhe Fei ◽  
Ji Zhu ◽  
Moulinath Banerjee ◽  
Yi Li
Keyword(s):  
Linear Models ◽  
High Dimensional ◽  
Partial Regression

Variable selection in high-dimensional double generalized linear models

2012 ◽  
Vol 55 (2) ◽  
pp. 327-347 ◽  
Author(s):  
Dengke Xu ◽  
Zhongzhan Zhang ◽  
Liucang Wu
Keyword(s):  
Variable Selection ◽  
Generalized Linear Models ◽  
Linear Models ◽  
High Dimensional

scholarly journals Grouping strategies and thresholding for high dimensional linear models

2013 ◽  
Vol 143 (9) ◽  
pp. 1417-1438 ◽  
Author(s):  
Mathilde Mougeot ◽  
Dominique Picard ◽  
Karine Tribouley
Keyword(s):  
Linear Models ◽  
High Dimensional ◽  
Grouping Strategies

scholarly journals On the accuracy in high‐dimensional linear models and its application to genomic selection

2018 ◽  
Vol 46 (1) ◽  
pp. 289-313
Author(s):  
Charles‐Elie Rabier ◽  
Brigitte Mangin ◽  
Simona Grusea
Keyword(s):  
Genomic Selection ◽  
Linear Models ◽  
High Dimensional

Optimal Estimation of Genetic Relatedness in High-Dimensional Linear Models

2018 ◽  
Vol 114 (525) ◽  
pp. 358-369 ◽  
Author(s):  
Zijian Guo ◽  
Wanjie Wang ◽  
T. Tony Cai ◽  
Hongzhe Li
Keyword(s):  
Linear Models ◽  
Genetic Relatedness ◽  
Optimal Estimation ◽  
High Dimensional
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