Asymptotic normality of the time-domain generalized least squares\n estimator for linear regression models

2019/02/08 by Hien D. Nguyen, Nguyen, Hien D
Engineering · Mathematics · #Advanced Statistical Methods and Models #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Inference #Statistical and numerical algorithms #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1902.03347

openalex publication_date 2019/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In linear models, the generalized least squares (GLS) estimator is applicable\nwhen the structure of the error dependence is known. When it is unknown, such\nstructure must be approximated and estimated in a manner that may lead to\nmisspecification. The large-sample analysis of incorrectly-specified GLS (IGLS)\nestimators requires careful asymptotic manipulations. When performing\nestimation in the frequency domain, the asymptotic normality of the IGLS\nestimator, under the so-called Grenander assumptions, has been proved for a\nbroad class of error dependence models. Under the same assumptions, asymptotic\nnormality results for the time-domain IGLS estimator are only available for a\nlimited class of error structures. We prove that the time-domain IGLS estimator\nis asymptotically normal for a general class of dependence models.\n

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