## The Annals of Mathematical Statistics

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

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

#### 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