THE LIL FOR THE ESTIMATES OF THE PARAMETERS IN A PARTLY LINEAR REGRESSION MODEL

Abstract

Consider the partly linear regression model $Y_i=X_i^\tau\beta+g(T_i)+\varepsilon_i$ $(i=1,\ldots,n)$, where $(X_i, T_i)$ are i.i.d. random design points, $\beta$ is a $p$-dimensional unknown parameter, $g(\cdot)$ is an unknown function on $[0, 1],$ $\varepsilon_i$ are i.i.d. random errors with mean 0 and variance $\sigma^2$. This paper is concerned with the {\bf LIL} of the estimators of $\beta$ and $\sigma^2.$