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Iterative maximum‐likelihood estimation of parameters of the Toeplitz correlation structure
Author(s) -
Mukherjee Bishwa Nath,
Maiti Sadhan Samar
Publication year - 1988
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1988.tb00888.x
Subject(s) - toeplitz matrix , mathematics , computation , iterative method , simple (philosophy) , matrix (chemical analysis) , covariance matrix , maximum likelihood , correlation , estimation theory , algorithm , statistics , pure mathematics , philosophy , materials science , geometry , epistemology , composite material
A simple iterative algorithm is proposed for obtaining the maximum‐likelihood estimates (m.l.e.) of the parameters of the symmetric Toeplitz or Laurent correlation matrix. A numerical example based on real‐life data is provided to illustrate the computation involved in the estimation and to demonstrate the feasibility of the proposed algorithm. This paper also provides expression in explicit form for the computation of the asymptotic dispersion matrix of the MLE. For comparative purposes, the Toeplitz correlation hypothesis as also other structural hypotheses have been tested and the results are discussed. The use of the proposed method in estimating the elements of Σ in the first step and then the possibility of using this estimated Σ for deriving a generalized least square estimate of the regression coefficients is pointed out.