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...

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...

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...

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...

In this note, we revisit the single-index model with heteroscedastic error, and recommend an estimating equation method in terms of transferring restricted least squares to unrestricted least squares: the estimator of the index parameter is asymptotically more efficient than existing estimators...

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...

In this paper, we consider a linear mixed-effects model with measurement errors in both fixed and random effects and find the moment of estimators for the parameters of interest. The strong consistency and asymptotic normality of the estimators are obtained under regularity conditions. Moreover,...

In this paper, we suggest an estimating equations based approach to study a general single-index model with a given out-layer link for longitudinal data and treat the classical one as its special case. Within a wide range of bandwidths which is for estimating the inner-layer nonparametric link,...