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| 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. |
| 关键词: 线性随机场 中偏差原理 经验周期图 |
| DOI： |
| 分类号:0211.4;0211.61 |
| 基金项目: |
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| MODERATE DEVIATIONS FOR EMPIRICAL PERIODOGRAM OF LINEAR RANDOM FIELDS |
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ZHANG Shi-ling
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| Abstract: |
| 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]. |
| Key words: linear random fields moderate deviation principle empirical periodogram |
