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Consistency of several variants of the standardized time series area variance estimator
Author(s) -
Damerdji Halim,
Goldsman David
Publication year - 1995
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(199512)42:8<1161::aid-nav3220420804>3.0.co;2-2
Subject(s) - estimator , mathematics , consistency (knowledge bases) , series (stratigraphy) , statistics , variance (accounting) , minimum variance unbiased estimator , efficient estimator , confidence interval , delta method , consistent estimator , bias of an estimator , convergence (economics) , mean squared error , econometrics , discrete mathematics , paleontology , accounting , economics , business , biology , economic growth
In statistical analysis of stationary time series or in steady‐state simulation output analysis, it is desired to find consistent estimates of the process variance parameter. Here, we consider variants of the area estimator of standardized time series, namely, the weighted area and the Cramér‐von Mises area estimators, and provide their consistency, in the strong sense and mean‐square sense. A sharp bound for the (asymptotic) variance of these estimators is obtained. We also present a central limit theorem for the weighted area estimator: this gives a rate of convergence of this estimator, as well as a confidence interval for the variance parameter. © 1995 John Wiley & Sons, Inc.