In this paper we aim to estimate the direction in general single-index models and to select important variables simultaneously when a diverging number of predictors are involved in regressions. Towards this end, we propose the nonconcave penalized inverse regression method. Specifically, the...

In this paper, we consider a semiparametric modeling with multi-indices when neither the response nor the predictors can be directly observed and there are distortions from some multiplicative factors. In contrast to the existing methods in which the response distortion deteriorates estimation...

For semiparametric models, one of the key issues is to reduce the predictors' dimension so that the regression functions can be efficiently estimated based on the low-dimensional projections of the original predictors. Many sufficient dimension reduction methods seek such principal projections...

In this paper we aim to construct adaptive confidence region for the direction of [xi] in semiparametric models of the form Y=G([xi]TX,[epsilon]) where G([dot operator]) is an unknown link function, [epsilon] is an independent error, and [xi] is a pnx1 vector. To recover the direction of [xi],...

The research described herein was motivated by a study of the relationship between the performance of students in senior high schools and at universities in China. A special linear structural equation model is established, in which some parameters are known and both the responses and the...

In this paper, we use the kernel method to estimate sliced average variance estimation (SAVE) and prove that this estimator is both asymptotically normal and root n consistent. We use this kernel estimator to provide more insight about the differences between slicing estimation and other...

Because highly correlated data arise from many scientific fields, we investigate parameter estimation in a semiparametric regression model with diverging number of predictors that are highly correlated. For this, we first develop a distribution-weighted least squares estimator that can recover...