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December, 1972 Order of Dependence in a Stationary Normally Distributed Two-Way Series
P. K. Bhattacharya
Ann. Math. Statist. 43(6): 1792-1807 (December, 1972). DOI: 10.1214/aoms/1177690852


Order of dependence is defined in a normally distributed two-way series. Under certain stationarity and symmetry conditions it is shown that when the extents of the series in both directions are large in comparison with the order of dependence, the joint density function reduces to a simple form with a small number of parameters after some adjustments. In this form a central role is played by the Kronecker products of some matrices having common eigenvectors. Maximum likelihood estimates of the parameters and likelihood ratio test criteria for certain hypotheses on order of dependence are derived.


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P. K. Bhattacharya. "Order of Dependence in a Stationary Normally Distributed Two-Way Series." Ann. Math. Statist. 43 (6) 1792 - 1807, December, 1972.


Published: December, 1972
First available in Project Euclid: 27 April 2007

MathSciNet: MR378322
zbMATH: 0298.62023
Digital Object Identifier: 10.1214/aoms/1177690852

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 6 • December, 1972
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