基于线性模型平均估计的置信区间

王苗苗

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (10) : 1866-1881.

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PDF(419 KB)
系统科学与数学 ›› 2020, Vol. 40 ›› Issue (10) : 1866-1881. DOI: 10.12341/jssms13985
论文

基于线性模型平均估计的置信区间

    王苗苗
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Confidence Interval Based on Model Average Estimator for Linear Regression

    WANG Miaomiao
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文章历史 +

摘要

已有的关于模型平均估计渐近分布理论的研究多是基于局部误设定的 假设, Hjort和Claeskens (2003)是其中最著名的文章之一. 虽然利用局部误设定 的假设可以证明模型平均估计渐近分布理论, 但是 ~Raftery~和~Zheng (2003)等对此假设提出了不合理性质疑和解释. 文章研究Hjort和Claeskens (2003)中的置信区间估计方法. 证明了在一般参 数设定下, 虽然Hjort和Claeskens (2003)中的渐近分布理论不一定成立, 但是关于不确定参数的线性函数的置信区间在正态分布误差、线性回归模 型下是有效的, 即置信区间的覆盖率趋于预设定的名义水平. 文章通过模拟研究进一步验证了理论结果.

Abstract

Most investigations on statistical inferences based on model averaging estimators have been conducted under the local misspecification assumption. Hjort and Claeskens (2003) is one of the most famous articles. However, although the local misspecification assumption provides a suitable framework for studying the asymptotic properties of frequentist model averaging estimators, Raftery and Zheng (2003) have raised doubts and explanations for this assumption. In this paper, we study the confidence interval estimation methods in Hjort and Claeskens (2003). It is proved that under general fixed parameter setup, although the asymptotic distribution theory in Hjort and Claeskens (2003) is not necessarily true, the confidence interval construction method for linear functions of uncertain parameters is still asymptotically valid in linear regression with normally distributed error. This means that the coverage probability of the confidence interval tends to the nominal level. Our simulation results support the theoretical conclusion.

关键词

模型平均 / 置信区间 / 渐近分布 / 线性回归.

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王苗苗. 基于线性模型平均估计的置信区间. 系统科学与数学, 2020, 40(10): 1866-1881. https://doi.org/10.12341/jssms13985
WANG Miaomiao. Confidence Interval Based on Model Average Estimator for Linear Regression. Journal of Systems Science and Mathematical Sciences, 2020, 40(10): 1866-1881 https://doi.org/10.12341/jssms13985
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