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随机回归模型的残差经验过程及时间序列应用AI 解读

Motivated by Gaussian tests for a time series, we are led to investigate the asymptotic behavior of the residual empirical processes of stochastic regression models. These models cover the fixed design regression models as well as general AR$(q)$ models. Since the number of the regression coeffi-cients is allowed to grow as the sample size increases, the obtained results are also applicable to nonlinear regression and stationary AR$(\infty)$ models. In this paper, we first…

线性过程自相关的序贯估计AI 解读

This paper considers sequential point estimation of the autocorrelations of stationary linear processes within the framework of the sequential procedure initiated by Robbins. The sequential estimator proposed here is based on the usual sample autocorrelations and is shown to be risk efficient in the sense of Starr as the cost per observation approaches zero. To achieve the asymptotic risk efficiency, we are led to study the uniform integrability and random central limit…