Estimation for a Semimartingale Regression Model Using the Method of Sieves

Abstract

Estimation by the method of sieves for a semimartingale regression model introduced by Aalen (1980) is studied. It is of interest to estimate functions which describe the influence of the covariates over time. An estimator for these functions is introduced and conditions which ensure consistency of the estimator in $L^2$-norm are given. Applications to diffusion processes and point processes with censored data are also discussed.