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 |
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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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