In this paper, we conduct simultaneous inference of the non-parametric part of a partially linear model when the non-parametric component is a multivariate unknown function. Based on semi-parametric estimates of the model, we construct a simultaneous confidence region of the multivariate...

In this paper, we analyze the nonparametric part of a partially linear model when the covariates in parametric and non-parametric parts are subject to measurement errors. Based on a two-stage semi-parametric estimate, we construct a uniform confidence surface of the multivariate function for...

This paper proposes a nonparametric test of causality in quantile. Zheng (1998) has proposed an idea to reduce the problem of testing a quantile restriction to a problem of testing a particular type of mean restriction in independent data. We extend Zheng's approach to the case of dependent...

We consider theoretical bootstrap "coupling" techniques for nonparametric robust smoothers and quantile regression, and verify the bootstrap improvement. To cope with curse of dimensionality, a variant of "coupling" bootstrap techniques are developed for additive models with both symmetric error...

We propose marginal integration estimation and testing methods for the coefficients of varying coefficient multivariate regression model. Asymptotic distribution theory is developed for the estimation method which enjoys the same rate of convergence as univariate function estimation. For the...

How can we measure and compare the relative performance of production units? If input and output variables are one dimensional, then the simplest way is to compute efficiency by calculating and comparing the ratio of output and input for each production unit. This idea is inappropriate though,...

Measuring dependence in a multivariate time series is tantamount to modelling its dynamic structure in space and time. In the context of a multivariate normally distributed time series, the evolution of the covariance (or correlation) matrix over time describes this dynamic. A wide variety of...

We consider two semiparametric models for the weight function in a biased sample model. The object of our interest parametrizes the weight function, and it is either Euclidean or non Euclidean. One of the models discussed in this paper is motivated by the estimation the mixing distribution of...

Generalized additive models (GAM) are multivariate nonparametric regressions for non-Gaussian responses including binary and count data. We propose a spline-backfitted kernel (SBK) estimator for the component functions. Our results are for weakly dependent data and we prove oracle efficiency....

The paper gives an overview on generalized linear models and its application in different branches of science. We introduce semiparametric extensions of the generalized linear model. One particular model of interest is the generalized partially linear model which allows a nonparametric modeling...