线性随机场的经验周期图的中偏差  

MODERATE DEVIATIONS FOR EMPIRICAL PERIODOGRAM OF LINEAR RANDOM FIELDS

作　　者：张施灵 ZHANG Shi-ling(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2023年第2期126-134,共9页Journal of Mathematics

摘　　要：在本文中,我们证明了线性随机场的二次形和经验周期图的中偏差.关于线性随机场的主要假设是驱动随机变量的对数Sobolev不等式和谱密度的一些可积条件.作为统计应用,我们给出了单边自回归平稳场的最小二乘估计和Yule-Walker估计的中偏估差计.上述结论是对文献[8]中线性随机过程的结论的推广.In this paper,we prove moderate deviations for quadratic forms and empirical periodograms of linear random fields.The main assumptions on the linear random fields are a Logarithmic Sobolev Inequality for the driving random variables and some integrability conditions for the spectral density.As statistical applications,we give the moderate deviation estimates of the least square and the Yule-Walker estimators for unilateral autoregression stationary fields.The results above are generalizations of the results for linear random processes in[8].

关 键 词：线性随机场 中偏差原理 经验周期图 

分 类 号：O211.4[理学—概率论与数理统计] O211.61[理学—数学]