On the estimation of the regression coefficients of a continuous parameter process with stationary residual

Expand
  • School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;

Published date: 05 Jun 2006

Abstract

The asymptotic expressions of the covariance matrices for both the least square estimates LαT and Markov (best linear) estimates âT are obtained, based on a sample in a finite interval (0, T) of the regression coefficientsα = (α1, · · · , αm0) 2 of a parameter-continuous process with a stationary residual. We assume that the regression variables ψν(t), t "e 0, ν = 1, · · · ,m0, are continuous in t, and satisfy conditions (3.1) - (3.3). For the residual, we assume that it is a stationary process that possesses a bounded continuous spectral density f(λ). Under these assumptions, it is proven that image,where the matrices DT, B(0), α(λ) are defined in Section 3. Under the assumptions mentioned above, if, furthermore, there exist some positive integer m and a constant C such that g(λ)(1+λ2)m "e C > 0, where g(λ) is the spectral density of the residual, and for every N >0, image converge uniformly in h, l "(-N,N), then the following formula holds. imageThe asymptotic equivalence of the least square estimates and the Markov estimates is also discussed.

Cite this article

YAN Shi-jian(Yien Sze-Chien), YAN Shi-jian(Yien Sze-Chien), LIU Xiu-fang(Liu Hsiu-Fang), LIU Xiu-fang(Liu Hsiu-Fang) . On the estimation of the regression coefficients of a continuous parameter process with stationary residual[J]. Frontiers of Mathematics in China, 2006 , 1(2) : 201 -233 . DOI: 10.1007/s11464-006-004-z

Outlines

/