A dimension reduction based approach for estimation and variable selection in partially linear single-index models with high-dimensional covariates

DOI10.1214/12-EJS744zbMath1295.62046OpenAlexW2075101818MaRDI QIDQ1950897

Jun Zhang, Hua Liang, Tao Wang, Li Xing Zhu

Publication date: 28 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ejs/1354284419

zbMATH Keywords

profile likelihoodsufficient dimension reductionpartially linear modelsinverse regressioncoordinate-independent sparse estimation (CISE)cumulative slicing estimationhigh-dimensional covariate

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Nonparametric regression and quantile regression (62G08) Asymptotic properties of nonparametric inference (62G20) General nonlinear regression (62J02)

Related Items

Confidence intervals for high-dimensional partially linear single-index models, Robust and efficient direction identification for groupwise additive multiple-index models and its applications, Estimation and variable selection for a class of quantile regression models with multiple index, Estimation and variable selection in partial linear single index models with error-prone linear covariates, Uniformly valid inference for partially linear high-dimensional single-index models, Statistical inference on restricted partial linear regression models with partial distortion measurement errors, Empirical likelihood for heteroscedastic partially linear single-index models with growing dimensional data, Partial linear modelling with multi-functional covariates, Unnamed Item, Detection of the symmetry of model errors for partial linear single-index models, Estimating the conditional single-index error distribution with a partial linear mean regression

Uses Software

• hgam

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Estimation and testing for partially linear single-index models
• Sliced Regression for Dimension Reduction
• Coordinate-independent sparse sufficient dimension reduction and variable selection
• The EFM approach for single-index models
• Robust rank correlation based screening
• Automatic model selection for partially linear models
• Estimation for a partial-linear single-index model
• Component selection and smoothing in multivariate nonparametric regression
• Variable selection in nonparametric additive models
• Covariance regularization by thresholding
• SCAD-penalized regression in high-dimensional partially linear models
• Semiparametric and nonparametric methods in econometrics
• High-dimensional additive modeling
• Sparsistency and rates of convergence in large covariance matrix estimation
• Convergence rates for parametric components in a partly linear model
• Efficient estimates in semiparametric additive regression models with unknown error distribution
• Semiparametric least squares (SLS) and weighted SLS estimation of single-index models
• Estimation in a semiparametric partially linear errors-in-variables model
• Asymptotics for kernel estimate of sliced inverse regression
• Nonconcave penalized likelihood with a diverging number of parameters.
• Optimal smoothing in single-index models
• Regularized estimation of large covariance matrices
• Semi-parametric estimation of partially linear single-index models
• Single-index model selections
• On Distribution-Weighted Partial Least Squares with Diverging Number of Highly Correlated Predictors
• Asymptotic properties of sufficient dimension reduction with a diverging number of predictors
• Adaptive Thresholding for Sparse Covariance Matrix Estimation
• Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models
• Approximation Theorems of Mathematical Statistics
• Sufficient dimension reduction through discretization-expectation estimation
• On Directional Regression for Dimension Reduction
• Sliced Inverse Regression for Dimension Reduction
• On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma
• Added-Variable Plots and Curvature in Linear Regression
• Graphics for Regressions With a Binary Response
• Generalized Partially Linear Single-Index Models
• Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
• Penalized Spline Estimation for Partially Linear Single-Index Models
• An Adaptive Estimation of Dimension Reduction Space
• Dimension Reduction for the Conditionalkth Moment in Regression
• Dimension Reduction in Regressions Through Cumulative Slicing Estimation
• Optimization algorithms exploiting unitary constraints
• Sparse sufficient dimension reduction
• Estimation in Partially Linear Models With Missing Covariates
• On Sliced Inverse Regression With High-Dimensional Covariates