Efficient density estimation in an AR(1) model

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY
Anton Schick, Wolfgang Wefelmeyer
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引用次数: 0

Abstract

This paper studies a class of plug-in estimators of the stationary density of an autoregressive model with autoregression parameter 0<ϱ<1. These use two types of estimator of the innovation density, a standard kernel estimator and a weighted kernel estimator with weights chosen to mimic the condition that the innovation density has mean zero. Bahadur expansions are obtained for this class of estimators in L1, the space of integrable functions. These stochastic expansions establish root-n consistency in the L1-norm. It is shown that the density estimators based on the weighted kernel estimators are asymptotically efficient if an asymptotically efficient estimator of the autoregression parameter is used. Here asymptotic efficiency is understood in the sense of the Hájek–Le Cam convolution theorem.
AR(1)模型的有效密度估计
研究了一类自回归参数为0<ϱ<1的自回归模型平稳密度的插入估计量。这些方法使用了两种类型的创新密度估计量,一种是标准核估计量,另一种是加权核估计量,其权重选择来模拟创新密度均值为零的情况。在可积函数空间L1中,得到了这类估计量的Bahadur展开式。这些随机展开式在l1范数中建立了根n一致性。如果使用自回归参数的渐近有效估计量,则表明基于加权核估计量的密度估计量是渐近有效的。这里的渐近效率是在Hájek-Le Cam卷积定理的意义上理解的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Electronic Journal of Statistics
Electronic Journal of Statistics STATISTICS & PROBABILITY-
CiteScore
1.80
自引率
9.10%
发文量
100
审稿时长
3 months
期刊介绍: The Electronic Journal of Statistics (EJS) publishes research articles and short notes on theoretical, computational and applied statistics. The journal is open access. Articles are refereed and are held to the same standard as articles in other IMS journals. Articles become publicly available shortly after they are accepted.
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