Oracally Efficient Estimation and Consistent Model Selection for Spatial ARMA Process With Bivariate Trend
提出两步估计法处理含双变量趋势和空间自回归移动平均误差的非平稳空间过程，证明修正极大似然估计的甲骨文有效性和BIC模型选择的一致性，并通过模拟和实际数据验证。
ABSTRACT The analysis of nonlinearity in spatial and spatial‐temporal data continues to be a challenging topic. This article introduces a two‐step estimation procedure for modeling nonstationary spatial processes that comprise a smooth bivariate trend function and a spatial autoregressive and moving average (SRAMA) error term. To remove the bivariate trend from the observed process, we apply the cutting‐edge bivariate penalized spline method. The modified maximum likelihood estimator based on the residuals, as suggested by Yao and Brockwell (2006), is shown to be consistent and oracle efficient, achieving the same efficiency asymptotically as if the true trend function were known and removed to obtain the SARMA errors. Furthermore, we establish the consistency of Bayesian information criteria for model selection concerning the residual sequence. The finite sample performance of the proposed approach is evaluated with simulations and real data.