YAN Shi-jian(Yien Sze-Chien), YAN Shi-jian(Yien Sze-Chien), LIU Xiu-fang(Liu Hsiu-Fang), LIU Xiu-fang(Liu Hsiu-Fang)
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 coefficients
α = (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](/webpub/service/fcktest/UserFiles/Image/123.jpg)
,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](/webpub/service/fcktest/UserFiles/Image/ooo3}.jpg)
converge uniformly in
h, l "(-N,N), then the following formula holds.
![image](/webpub/service/fcktest/UserFiles/Image/oool.jpg)
The asymptotic equivalence of the least square estimates and the Markov estimates is also discussed.