In this Note, we study the linear part of the semi-parametric regression model defined by Yi=Zi?β+∑j=1dmj(Xij)+εi, 1≤i≤n, where Z_i=(Z_(i1), ..., Z_(ip))?, X_i=(X_(i1), ..., X_(id))~? are vectors of explanatory variables, β=(β_1, ... β_p)~? is a vector of unknown parameters, m_1, ..., _md are unknown univariate real functions, and ε_1, ..., ε_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 (mj)1≤j≤d and the least-square error criterion to estimate the parameter β, we establish the asymptotic normality together with the iterated logarithm law of the estimate β? of β.
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