Asymptotic results for the linear parameter estimate in partially linear additive regression model

作者：Chokri Khalid^*; Louani Djamal

来源：Comptes Rendus Mathematique, 2011, 349(19-20): 1105-1109.

DOI：10.1016/j.crma.2011.09.010

In this Note, we study the linear part of the semi-parametric regression model defined by Y(i) = Z(i)(inverted perpendicular)beta +Sigma(d)(j=1)m(j)(x(ij)) + epsilon(i), 1 <= i <= n, where Z(i) = (Z(i1), ... , Z(ip))(inverted perpendicular), X(i) = (X(i1), ... , X(id))(inverted perpendicular) are vectors of explanatory variables, beta = (beta(1), ... ,beta(p))(inverted perpendicular) is a vector of unknown parameters, m(1), ... , m(d) are unknown univariate real functions, and epsilon(1), ... , epsilon(n) are independent random modelling errors with mean zero and finite variances. Using the nonparametric kernel technique combined with the marginal integration method to estimate the functions (m(j))(1 <= j <= d) and the least-square error criterion to estimate the parameter beta, we establish the asymptotic normality together with the iterated logarithm law of the estimate (beta)over cap of beta.

• 出版日期2011-10