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A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a…
Non-random sample selection is a commonplace amongst many empirical studies and it appears when an output variable of interest is available only for a restricted non-random sub-sample of data. We introduce an extension of the generalized…
Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and…
This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we…
Empirical likelihood enables a nonparametric, likelihood-driven style of inference without restrictive assumptions routinely made in parametric models. We develop a framework for applying empirical likelihood to the analysis of experimental…
The generalized partially linear models on Riemannian manifolds are introduced. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for response variables…
In this paper we shall consider one parametric generalization of some non-symmetric divergence measures. The \textit{non-symmetric divergence measures} are such as: Kullback-Leibler \textit{relative information}, $\chi…
Generalized linear models are widely used in many areas of knowledge. As in other classes of regression models, it is desirable to perform diagnostic analysis in generalized linear models using residuals that are approximately standard…
This paper develops a general methodology to conduct statistical inference for observations indexed by multiple sets of entities. We propose a novel multiway empirical likelihood statistic that converges to a chi-square distribution under…
Nonparametric generalized likelihood ratio test is popularly used for model checking for regressions. However, there are two issues that may be the barriers for its powerfulness. First, the bias term in its liming null distribution causes…
We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the…
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…
The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted $L_2$-distance between the empirical characteristic functions of…
This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and…
This paper proposes a regularized pairwise difference approach for estimating the linear component coefficient in a partially linear model, with consistency and exact rates of convergence obtained in high dimensions under mild scaling…
In this paper, we study the nonparametric linear model, when the error process is a dependent Gaussian process. We focus on the estimation of the mean vector via a model selection approach. We first give the general theoretical form of the…
Neural networks are powerful predictive models, but they provide little insight into the nature of relationships between predictors and outcomes. Although numerous methods have been proposed to quantify the relative contributions of input…
The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…