A practical procedure for estimation of linear models via asymptotic quasi-likelihood. Issue 1 (1999)

• Record Type: Journal Article
• Authors: Biondini, Riccardo; Lin, Yan-Xia; Mvoi, Sifa
• Is Part Of: Journal of applied mathematics & decision sciences. Volume 3:Issue 1(1999)
• Page Start: 21
• Page End: 39
• Publication Date: 1999
• Subjects: Operations research -- Periodicals; Mathematical models -- Periodicals; Statistics -- Periodicals; Quality control -- Periodicals; Mathematical models; Operations research; Quality control; Statistics; Periodicals; 519.05
• DOI: 10.1155/S1173912699000024
• Languages: English
• ISSNs: 1173-9126

Abstract

Abstract : This paper is concerned with the application of an asymptotic quasi-likelihood practical procedure to estimate the unknown parameters in linear stochastic models of the formy t = f t ( θ ) + M t ( θ ) ( t = 1, 2, .., T ), wheref t is a linear predictable process ofθ andM t is an error term such thatE ( M t | F t − 1 ) = 0 andE ( M t 2 | F t − 1 ) < ∞ andF is aσ -field generated from{ y s } s ≤ t . For this model, to estimate the parameterθ ∈ Θ, the ordinary least squares method is usually inappropriate (if there is only one observable path of{ y t } and ifE ( M t 2 | F t − 1 ) is not a constant) and the maximum likelihood method either does not exist or is mathematically intractable. If the finite dimensional distribution ofM t is unknown, to obtain a good estimate ofθ an appropriate predictable processg t should be determined. In this paper, criteria for determiningg t are introduced which, if satisfied, provide more accurate estimates of the parameters via the asymptotic quasi-likelihood method.