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| PARAMETER ESTIMATION OF SPATIAL AR MODEL |
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Citation： |
Jiang Jiming.PARAMETER ESTIMATION OF SPATIAL AR MODEL[J].Chinese Annals of Mathematics B,1991,12(4):432~444 |
| Page view： 945
Net amount： 821 |
Authors： |
Jiang Jiming; |
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| Abstract： |
Consider a stable AR model of two parameter spatial series $\[\{ {X_t},t \in {N^2}\} ,i.e.\{ {X_t}:t \in {N^2}\} \]$ is homogeneous and satisfies the follow difference equation
$$\[{X_t} - \sum\limits_{s \in <0,p]}^{} {{a_s}{X_{i - s}}} = {W_i},(t \in {N^2})\]$$
where $\[\{ {W_t},t \in {N^2}\} \]$ is a two parameter white noise and the notation $<0,p]$ expresses the set of two dimentional lattice points $\[\{ ({k_1},{k_2}):0 \le {k_1} \le {p_1},0 \le {k_2} \le {p_2}but({k_1},{k_2}) \ne (0,0)\} \]$ and furthermore two-varidble polynomial:
$$\[1 - \sum\limits_{({s_1},{s_2}) \in < 0,p]} \]\[{{a_{({s_1},{s_2})}}Z_1^{{k_1}}Z_2^{{s_2}} \ne 0(\left| {{Z_1}} \right| \le 1,\left| {{Z_2}} \right| \le 1).}\]$$
In this paper, under frirly general conditions (it is required that $\[\{ {W_t}\} \]$ satisfies the conditions of two-parameter martingale difference, which is much weaker than supposing-$\[\{ {W_t}\} \]$ to be i.i,d).the author obtains strong consistency and asymptotic normality of the Y-W(LS) estimate of the AR parameters $\[{\alpha _s}\]$ whenever $\[{n_1}{n_2} \to \infty \]$, where $\[{n_1}\]$ and $$ de\[{n_2}\]te the horizontal and vertical sampling width respectiyely. |
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