The Annals of Mathematical Statistics

Order of Dependence in a Stationary Normally Distributed Two-Way Series

P. K. Bhattacharya

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 43, Number 6 (1972), 1792-1807.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177690852

Digital Object Identifier
doi:10.1214/aoms/1177690852

Mathematical Reviews number (MathSciNet)
MR378322

Zentralblatt MATH identifier
0298.62023

JSTOR
links.jstor.org

Citation

Bhattacharya, P. K. Order of Dependence in a Stationary Normally Distributed Two-Way Series. Ann. Math. Statist. 43 (1972), no. 6, 1792--1807. doi:10.1214/aoms/1177690852. https://projecteuclid.org/euclid.aoms/1177690852


Export citation