Large sample theory of the estimation of the error distribution for a semiparametric model

The paper studies large sample theory of estimators of the error distribution for the semiparametric model Y = X(T)beta + g(T) + epsilon. Under appropriate conditions, we prove that the estimators converge in probability, converge almost surely and converge uniformly almost surely. Asymptotic normality and the rates of convergence of the estimators are also investigated. Finally we establish the law of the iterated logarithm for the estimators.