Yuanyuan Zhang

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.

The optimal subsampling is an statistical methodology for generalized linear models (GLMs) to make inference quickly about parameter estimation in massive data regression. Existing literature only considers bounded covariates. In this paper, the asymptotic normality of the subsampling M-estimator based on the Fisher information matrix is obtained. Then, we study the asymptotic properties of subsampling estimators of unbounded GLMs with nonnatural links, including conditional asymptotic properties and unconditional asymptotic properties.