REAL

Asymptotic inference for an unstable spatial AR model

Baran, Sándor and Pap, Gyula and van Zuijlen, Martien C. A. (2004) Asymptotic inference for an unstable spatial AR model. Statistics, 38 (6). pp. 465-482. ISSN 0233-1888

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Abstract

The spatial autoregressive process X-k,X-l = alpha(X-k-1,X-l + X-k,X-l-1) + epsilon(k,l), where k, l greater than or equal to 1 is investigated. We consider the least squares estimator alpha(m,n) of alpha based on the observations {X-k,X-l: 1 less than or equal to k less than or equal to m and 1 less than or equal to e less than or equal to n}. In the stable (i.e. asymptotically stationary) case, when \alpha\ < 1/2, asymptotic normality (mn)(1/2)(alpha(m,n) - alpha) -->(D) N (0, sigma(alpha)(2)) as m, n --> infinity with m/n --> constant > 0 can be derived from the previous more general results due to Basu and Reinsel (1992, 1993, 1994). In the unstable case, when la I = 1/2, we prove again asymptotic normality, but (in contrast to the doubly geometric spatial model) with a surprising rate of convergence, namely (mn)(5/8)(alpha(m,n) - alpha) -->(D) N(0, sigma(2)) as in, n --> infinity with m/n --> constant > 0.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika
Depositing User: Erika Bilicsi
Date Deposited: 08 Apr 2013 13:40
Last Modified: 08 Apr 2013 13:40
URI: http://real.mtak.hu/id/eprint/4675

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