Asymptotic Theory for Sieve Estimators in Semimartingale Regression Models.

Abstract : This paper studies the estimation of functions alpha sub 1, ..., alpha sub p describing the temporal influence of p covariate processes in a regression model for semi-martingales. McKeague (1986) introduced sieve estimators for alpha sub 1, ..., alpha sub p and established consistency in sq l-norm. In this paper the asymptotic distribution theory for the integrated sieve estimators is developed. Smoothed sieve estimators are shown to be pointwise consistent and rates of convergence are provided. (Author)