超高维数据边际经验似然独立筛选方法（英文）

可加模型通过协变量函数对响应变量起作用,是更加灵活的非参统计模型.当协变量个数大于样本数且以指数阶增大时,将维数降到经典方法可解决的范围是统计学家急需解决的问题.本文研究了超高维数据可加模型的变量筛选问题,提出了边际经验似然变量筛选方法.该方法通过排列在0点的边际经验似然率选择变量.我们证明了选择变量集以概率1渐进包含真实变量集;提出了迭代边际经验似然变量筛选方法.数据模拟和实数据分析验证了所提方法的可行性.

Statistical inference on parametric part for partially linear single-index model

Statistical inference on parametric part for the partially linear single-index model (PLSIM) is considered in this paper. A profile least-squares technique for estimating the parametric part is proposed and the asymptotic normality of the profile least-squares estimator is given. Based on the estimator, a generalized likelihood ratio (GLR) test is proposed to test whether parameters on linear part for the model is under a contain linear restricted condition. Under the null model, the proposed GLR statistic follows asymptotically the χ2-distribution with the scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Both simulated and real data examples are used to illustrate our proposed methods.

The Adaptive LASSO Spline Estimation of Single-Index Model

In this paper, based on spline approximation, the authors propose a unified variable selection approach for single-index model via adaptive L1 penalty. The calculation methods of the proposed estimators are given on the basis of the known lars algorithm. Under some regular conditions, the authors demonstrate the asymptotic properties of the proposed estimators and the oracle properties of adaptive LASSO(aL ASSO) variable selection. Simulations are used to investigate the performances of the proposed estimator and illustrate that it is effective for simultaneous variable selection as well as estimation of the single-index models.

Feature Screening for Nonparametric and Semiparametric Models with Ultrahigh-Dimensional Covariates

This paper considers the feature screening and variable selection for ultrahigh dimensional covariates. The new feature screening procedure base on conditional expectation which is used to differentiate whether an explanatory variable contributes to a response variable or not, without requiring a specific parametric form of the underlying data model. The authors estimate the marginal condi- tional expectation by kernel regression estimator. The proposed method is showed to have sure screen property. The authors propose an iterative kernel estimator algorithm to reduce the ultrahigh dimensionality to an appropriate scale. Simulation results and real data analysis demonstrate the proposed method works well and performs better than competing methods.

Variable Selection of Varying Dispersion Student-t Regression Models

The Student-t regression model is a useful extension of the normal model,which can be used for statistical modeling of data sets involving errors with heavy tails and/or outliers and provides robust estimation of means and regression coefficients.In this paper,the varying dispersion Student-t regression model is discussed,in which both the mean and the dispersion depend upon explanatory variables.The problem of interest is simultaneously select significant variables both in mean and dispersion model.A unified procedure which can simultaneously select significant variable is given.With appropriate selection of the tuning parameters,the consistency and the oracle property of the regularized estimators are established.Both the simulation study and two real data examples are used to illustrate the proposed methodologies.

Sequential Feature Screening for Generalized Linear Models with Sparse Ultra-High Dimensional Data

This paper considers the iterative sequential lasso(ISLasso)variable selection for generalized linear model with ultrahigh dimensional feature space.The ISLasso selects features by estimated parameter sequentially iteratively for the second order approximation of likelihood function where the features selected depend on regulatory parameters.The procedure stops when extended BIC(EBIC)reaches a minimum.Simulation study demonstrates that the new method is a desirable approach over other methods.

Partially Linear Single-Index Model in the Presence of Measurement Error

The partially linear single-index model(PLSIM) is a flexible and powerful model for analyzing the relationship between the response and the multivariate covariates. This paper considers the PLSIM with measurement error possibly in all the variables. The authors propose a new efficient estimation procedure based on the local linear smoothing and the simulation-extrapolation method,and further establish the asymptotic normality of the proposed estimators for both the index parameter and nonparametric link function. The authors also carry out extensive Monte Carlo simulation studies to evaluate the finite sample performance of the new method, and apply it to analyze the osteoporosis prevention data.

Hierarchically penalized additive hazards model with diverging number of parameters

In many applications,covariates can be naturally grouped.For example,for gene expression data analysis,genes belonging to the same pathway might be viewed as a group.This paper studies variable selection problem for censored survival data in the additive hazards model when covariates are grouped.A hierarchical regularization method is proposed to simultaneously estimate parameters and select important variables at both the group level and the within-group level.For the situations in which the number of parameters tends to∞as the sample size increases,we establish an oracle property and asymptotic normality property of the proposed estimators.Numerical results indicate that the hierarchically penalized method performs better than some existing methods such as lasso,smoothly clipped absolute deviation(SCAD)and adaptive lasso.

Testing for the parametric parts in a single-index varying-coefficient model

Single-index varying-coefficient models (SIVCMs) are very useful in multivariate nonparametric regression.However,there has less attention focused on inferences of the SIVCMs.Using the local linear method,we propose estimates of the unknowns in the SIVCMs.In this article,our main purpose is to examine whether the generalized likelihood ratio (GLR) tests are applicable to the testing problem for the index parameter in the SIVCMs.Under the null hypothesis our proposed GLR statistic follows the chi-squared distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters or functions,which is called as Wilks' phenomenon (see Fan et al.,2001).A simulation study is conducted to illustrate the proposed methodology.

Integrated Square Error of Hazard Rate Estimation for Survival Data with Missing Censoring Indicators

The problem of hazard rate estimation under right-censored assumption has been investigated extensively.Integrated square error(ISE)of estimation is one of the most widely accepted measurements of the global performance for nonparametric kernel estimation.But there are no results available for ISE of hazard rate estimation under right-censored model with censoring indicators missing at random(MAR)so far.This paper constructs an imputation estimator of the hazard rate function and establish asymptotic normality of the ISE for the kernel hazard rate estimator with censoring indicators MAR.At the same time,an asymptotic representation of the mean integrated square error(MISE)is also presented.The finite sample behavior of the estimator is investigated via one simple simulation.

Estimation and Inference in Semi-Functional Partially Linear Measurement Error Models

This article studies the estimation and statistical inference problems of semi-functional partially linear regression models when the covariates in the linear part are measured with additive error. To obtain the estimation of the parametric component, a corrected profile least-squares based estimation procedure is developed. Asymptotic properties of the proposed estimators are established under some mild assumptions. To test hypothesis on the parametric part, the authors propose a novel test statistic based on the difference between the corrected residual sums of squares under the null and alternative hypotheses, and show that its limiting distribution is a weighted sum of independent standard χ12. Finally, the authors illustrate the finite sample performance of the methods with some simulation studies and a real data application.