线性随机场的经验周期图的中偏差

MODERATE DEVIATIONS FOR EMPIRICAL PERIODOGRAM OF LINEAR RANDOM FIELDS

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].