Measurement error in linear autoregressive models
Measurement error in linear autoregressive models
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DOI：
10.1198/016214504000001871
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发表时间：
2005-09-01
影响因子：
3.7
通讯作者：
Buonaccorsi, JR
中科院分区：
文献类型：
--
作者：
Staudenmayer, J;Buonaccorsi, JR
时间序列数据经常受到测量误差的影响，通常是由于需要估计感兴趣的变量的结果。尽管通常合理地假设测量误差是累加的(即，估计器对丢失的真值是有条件的无偏的)，但是测量误差方差通常由于总体/过程随时间的变化和/或采样努力的变化而变化。在这篇文章中，我们讨论了线性自回归模型中存在相加和不相关测量误差时的参数估计，允许测量误差方差中的异方差。我们建立了忽略测量误差的朴素估计的渐近性质，并提出了一种基于修正Yule-Walker估计方程的估计。我们还研究了基于正态假设的伪似然方法，并使用卡尔曼滤波进行了计算。我们回顾了已提出的其他技术，包括两种不需要测量误差方差信息的技术，并从理论上和通过模拟对各种估计器进行了比较。基于修正估计方程的估计器很容易获得，并且容易适应(并且对)不相等的测量误差方差具有鲁棒性。渐近计算和有限样本模拟表明，它往往是相对有效的。
Time series data are often subject to measurement error, usually the result of needing to estimate the variable of interest. Although it is often reasonable to assume that the measurement error is additive (i.e., the estimator is conditionally unbiased for the missing true value), the measurement error variances often vary as a result of changes in the population/process over time and/or changes in sampling effort. In this article we address estimation of the parameters in linear autoregressive models in the presence of additive and uncorrelated measurement errors, allowing heteroscedasticity in the measurement error variances. We establish the asymptotic properties of naive estimators that ignore measurement error and propose an estimator based on correcting the Yule-Walker estimating equations. We also examine a pseudo-likelihood method based on normality assumptions and computed using the Kalman filter. We review other techniques that have been proposed, including two that require no information about the measurement error variances, and compare the various estimators both theoretically and via simulations. The estimator based on corrected estimating equations is easy to obtain and readily accommodates (and is robust to) unequal measurement error variances. Asymptotic calculations and finite-sample simulations show that it is often relatively efficient.