This article is cited in 2 papers

MATHEMATICS

Estimation of the parametric regression with a pulse noise by discrete time observations

V. V. Konev^a, E. A. Pchelintsev<sup>bc

a</sup> Tomsk State University
^b Tomsk State University
^c Université de Rouen (France)

Abstract: The paper considers the problem of parametric estimation in a continuous time linear parametric regression model with a non-Gaussian Ornstein–Uhlenbeck process by discrete time observations. Improved estimates with smaller mean square risk as compared with the ordinary least square estimates are proposed for the unknown regression parameters. The asymptotic minimaxity of these estimates in the sense of the robust risk has been proved.

Keywords: non-Gaussian parametric regression, improved estimation, least square estimates, pulse noise, Ornstein–Uhlenbeck process, quadratic risk, minimaxity.

UDC: 517.16+519.2

Received: 31.01.2012