Moderate deviations of empirical periodogram and non-linear functionals of moving average processes
Moderate deviations of empirical periodogram and non-linear functionals of moving average processes
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DOI：
10.1016/j.anihpb.2005.04.006
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发表时间：
2006-07
影响因子：
1.5
通讯作者：
H. Djellout;A. Guillin;Liming Wu
中科院分区：
文献类型：
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作者：
H. Djellout;A. Guillin;Liming Wu
对于移动平均过程（或线性过程）的非线性泛函，建立了至多为二次增长的中等偏差原理。移动平均过程的主要假设是驱动随机变量的对数Sobolev不等式和连续性，或者谱密度的一些（较弱的）可积性条件（涵盖一些长距离依赖的情况）。我们还获得了经验周期图的中等偏差估计，展示了一种有趣的新形式的速率函数，即与高斯速率函数相比有一个校正项。作为统计应用，我们提供了平稳自回归过程参数的最小二乘和Yule-Walker估计的中等偏差估计，以及高斯情况下Neyman-Pearson似然比检验的估计。©2005 Elsevier SAS。版权所有。
A moderate deviation principle for non-linear functionals, with at most quadratic growth, of moving average processes (or linear processes) is established. The main assumptions on the moving average process are a Logarithmic Sobolev Inequality for the driving random variables and the continuity, or some (weaker) integrability condition on the spectral density (covering some cases of long range dependence). We also obtain the moderate deviation estimate for the empirical periodogram, exhibiting an interesting new form of the rate function, ie with a correction term compared to the Gaussian rate functional. As statistical applications we provide the moderate deviation estimates of the least square and the Yule–Walker estimators of the parameter of a stationary autoregressive process and of the Neyman–Pearson likelihood ratio test in the Gaussian case.© 2005 Elsevier SAS. All rights reserved.