Statistical tests in the partially linear additive regression models

In the present paper, we are mainly concerned with statistical tests in the partially linear additive model defined by Y-i = Z(i)(T)beta + Sigma(d)(l=1)m(l)(X-i,X-l) + epsilon(i), 1 <= i <= n, where Z(i) = (Z(i), (1), ... , Z(ip))(T) and X-i = (X-i,(1), ... , X-id)(T) are vectors of explanatory variables, beta = (beta(1), ... , beta(p))(T) is a vector of unknown parameters, m(1), ... , m(d) are unknown univariate real functions, and epsilon(1), ... , epsilon(n) are independent random errors with mean zero and finite variances sigma(2)(epsilon). More precisely, we first consider the problem of testing the null hypothesis beta = beta(0). The second aim of this paper is to propose a test for the null hypothesis H-0(sigma) : sigma(2)(epsilon) = sigma(2)(0), 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. (C) 2014 Elsevier B.V. All rights reserved.