Nonparametric kernel regression when the regressor follows a counting process

The regression model Y i = m(τ i ) + ε i where the the τ i can be thought of as times, is studied in a marked point process framework. This paper will show consistency and asymptotic normality for the Nadaraya-Watson kernel estimate of m(·) under Aalen's multiplicative intensity model for the τ i and provide some further results. The main contribution of the paper is the model formulation, which allows for quite general censoring schemes of the measurement times. The model appears useful for longitudinal data applications and is applied to repeated measurements of oestriol for 52 pregnant women, for a case where censoring is present.