To test heteroscedasticity in single index models, in this paper two test statistics are proposed via quadratic conditional moments. Without the use of dimension reduction structure, the first test has the usual convergence rate in nonparametric sense. Under the dimension reduction structure of...

In this paper, we investigate the empirical likelihood for constructing a confidence region of the parameter of interest in a multi-link semiparametric model when an infinite-dimensional nuisance parameter exists. The new model covers the commonly used varying coefficient, generalized linear,...

The purpose of this paper is two-fold. First, for the estimation or inference about the parameters of interest in semiparametric models, the commonly used plug-in estimation for infinite-dimensional nuisance parameter creates non-negligible bias, and the least favorable curve or under-smoothing...

How to sufficiently use the structure information behind the data is still a challenging issue. In this paper, a local linear–additive estimation and its relevant version are proposed to automatically capture the additive information for general multiple nonparametric regressions. Our method...

Inference for variance components in linear mixed models of ANOVA type, including estimation and testing, has been investigated when the number of fixed effects is fixed. However, for high-dimensional data, this number is large and would be regarded as a divergent value as the sample size goes...

In this paper, from the estimating equation-based sufficient dimension reduction method in the literature, its robust version is proposed to alleviate the impact from outliers. To achieve this, a robust nonparametric regression estimator is suggested. The estimator is plugged in the estimating...

Existing model-free tests of the conditional coordinate hypothesis in sufficient dimension reduction (Cook (1998) [3]) focused mainly on the first-order estimation methods such as the sliced inverse regression estimation (Li (1991) [14]). Such testing procedures based on quadratic inference...

In this paper, we consider subset deletion diagnostics for fixed effects (coefficient functions), random effects and one variance component in varying coefficient mixed models (VCMMs). Some simple updated formulas are obtained, and based on which, Cook's distance, joint influence and conditional...

Diagnostic checking for multivariate parametric models is investigated in this article. A nonparametric Monte Carlo Test (NMCT) procedure is proposed. This Monte Carlo approximation is easy to implement and can automatically make any test procedure scale-invariant even when the test statistic is...

The empirical likelihood method is especially useful for constructing confidence intervals or regions of parameters of interest. Yet, the technique cannot be directly applied to partially linear single-index models for longitudinal data due to the within-subject correlation. In this paper, a...