## The Annals of Statistics

### Estimation for a Semimartingale Regression Model Using the Method of Sieves

Ian W. McKeague

#### 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.

#### Article information

Source
Ann. Statist., Volume 14, Number 2 (1986), 579-589.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349939

Digital Object Identifier
doi:10.1214/aos/1176349939

Mathematical Reviews number (MathSciNet)
MR840515

Zentralblatt MATH identifier
0651.62084

JSTOR
links.jstor.org

Subjects
Primary: 62M09: Non-Markovian processes: estimation
Secondary: 62G05: Estimation 60G44: Martingales with continuous parameter

#### Citation

McKeague, Ian W. Estimation for a Semimartingale Regression Model Using the Method of Sieves. Ann. Statist. 14 (1986), no. 2, 579--589. doi:10.1214/aos/1176349939. https://projecteuclid.org/euclid.aos/1176349939