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We in this paper propose a directional regression based approach for ultrahigh dimensional sufficient variable screening with censored responses. The new method is designed in a model-free manner and thus can be adapted to various complex…
High-dimensional variable selection is an important issue in many scientific fields, such as genomics. In this paper, we develop a sure independence feature screening pro- cedure based on kernel canonical correlation analysis (KCCA-SIS, for…
We propose a novel and computationally efficient approach for nonparametric conditional density estimation in high-dimensional settings that achieves dimension reduction without imposing restrictive distributional or functional form…
Statistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to account for. A critical question remains unsettled; that is, is it possible…
The aim of this thesis is to find a solution to the non-parametric independence problem in separable metric spaces. Suppose we are given finite collection of samples from an i.i.d. sequence of paired random elements, where each marginal has…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
Consider the normal linear regression setup when the number of covariates p is much larger than the sample size n, and the covariates form correlated groups. The response variable y is not related to an entire group of covariates in all or…
Semiparametric single-index assumptions are convenient and widely used dimen\-sion reduction approaches that represent a compromise between the parametric and fully nonparametric models for regressions or conditional laws. In a mean…
The objective of the present paper is to develop a minimax theory for the varying coefficient model in a non-asymptotic setting. We consider a high-dimensional sparse varying coefficient model where only few of the covariates are present…
The large number of spectral variables in most data sets encountered in spectral chemometrics often renders the prediction of a dependent variable uneasy. The number of variables hopefully can be reduced, by using either projection…
Let X be a d dimensional vector of covariates and Y be the response variable. Under the nonparametric model Y = m(X) + {\sigma}(X) \in we develop an ANOVA-type test for the null hypothesis that a particular coordinate of X has no influence…
We consider a Gaussian sequence space model $X_{\lambda}=f_{\lambda} + \xi_{\lambda},$ where $\xi $ has a diagonal covariance matrix $\Sigma=\diag(\sigma_\lambda ^2)$. We consider the situation where the parameter vector $(f_{\lambda})$ is…
Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression…
In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…
Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity…
A new model-free screening method called the fused Kolmogorov filter is proposed for high-dimensional data analysis. This new method is fully nonparametric and can work with many types of covariates and response variables, including…
The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from…
The goal of this presentation is to build an efficient non-parametric Bayes classifier in the presence of large numbers of predictors. When analyzing such data, parametric models are often too inflexible while non-parametric procedures tend…
This paper studies nonparametric series estimation and inference for the effect of a single variable of interest x on an outcome y in the presence of potentially high-dimensional conditioning variables z. The context is an additively…