Linearity identification for general partial linear single-index models
type: Item
instance of: scholarly article
title: Linearity identification for general partial linear single-index models
zbMATH Open document ID: 1400.62067
DOI: 10.1155/2016/3537564
author: Luhong Wang
author: Shao-Gao Lv
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: Partial linear models, a family of popular semiparametric models, provide us with an interpretable and flexible assumption for modelling complex data. One challenging question in partial linear models is the structure identification for the linear components and the nonlinear components, especially for high dimensional data. This paper considers the structure identification problem in the general partial linear single-index models, where the link function is unknown. We propose two penalized methods based on a modern dimension reduction technique. Under certain regularity conditions, we show that the second estimator is able to identify the underlying true model structure correctly. The convergence rate of the new estimator is established as well.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62J12
zbMATH DE Number: 6953066
Wikidata QID: Q59130879
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/3537564
OpenAlex ID: W2524501495
cites work: Additive regression and other nonparametric models
cites work: Fitting a bivariate additive model by local polynomial regression
cites work: Additive partial linear models with measurement errors
cites work: Estimation and variable selection for generalized additive partial linear models
cites work: Estimation and variable selection for semiparametric additive partial linear models
cites work: Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates
cites work: Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models
cites work: Q3145537
cites work: Partially linear structure identification in generalized additive models with NP-dimensionality
cites work: Gradient-Based Kernel Dimension Reduction for Regression
cites work: Q3895980
cites work: Sliced Inverse Regression for Dimension Reduction
cites work: Comment
cites work: On Directional Regression for Dimension Reduction
cites work: Theory of Reproducing Kernels
cites work: Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
cites work: A coordinate gradient descent method for nonsmooth separable minimization
cites work: Minimax sparse principal subspace estimation in high dimensions
Recommended article: Estimation and testing for partially linear single-index models
Recommended article: Estimation for a partial-linear single-index model
Recommended article: Generalized Partially Linear Single-Index Models
Recommended article: Results concerning the generalized partially linear single-index model
Recommended article: Semi-parametric estimation of partially linear single-index models
Recommended article: Estimation and variable selection for generalised partially linear single-index models
Recommended article: Estimation for single-index and partially linear single-index integrated models
Recommended article: Efficient estimation for generalized partially linear single-index models
Recommended article: On extended partially linear single-index models
description: scientific article; zbMATH DE number 6953066