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High‐order Corrected Estimator of Asymptotic Variance with Optimal Bandwidth
Author(s) -
Chan Kin Wai,
Yau Chun Yip
Publication year - 2017
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12279
Subject(s) - estimator , mathematics , rate of convergence , statistics , delta method , smoothness , sample size determination , mean squared error , variance (accounting) , order statistic , markov chain , convergence (economics) , constant (computer programming) , computer science , computer network , mathematical analysis , channel (broadcasting) , accounting , economics , business , programming language , economic growth
Estimation of time‐average variance constant (TAVC), which is the asymptotic variance of the sample mean of a dependent process, is of fundamental importance in various fields of statistics. For frequentists, it is crucial for constructing confidence interval of mean and serving as a normalizing constant in various test statistics and so forth. For Bayesians, it is widely used for evaluating effective sample size and conducting convergence diagnosis in Markov chain Monte Carlo method. In this paper, by considering high‐order corrections to the asymptotic biases, we develop a new class of TAVC estimators that enjoys optimalL 2 ‐convergence rates under different degrees of the serial dependence of stochastic processes. The high‐order correction procedure is applicable to estimation of the so‐called smoothness parameter, which is essential in determining the optimal bandwidth. Comparisons with existing TAVC estimators are comprehensively investigated. In particular, the proposed optimal high‐order corrected estimator has the best performance in terms of mean squared error.