Statistical tests in the partially linear additive regression models.

Abstract: In the present paper, we are mainly concerned with statistical tests in the partially linear additive model defined by where and are vectors of explanatory variables, is a vector of unknown parameters, are unknown univariate real functions, and are independent random errors with mean zero and finite variances . More precisely, we first consider the problem of testing the null hypothesis . The second aim of this paper is to propose a test for the null hypothesis , in the partially linear additive regression models. Under the null hypotheses, the limiting distributions of the proposed test statistics are shown to be standard chi-squared distributions. Finally, simulation results are provided to illustrate the finite sample performance of the proposed statistical tests. [Copyright &y& Elsevier]