Overlapping Batch Means: Something more for Nothing?

Alexopoulos,; Goldsman,; Wilson, F. F.

doi:10.1109/wsc.2011.6147767

Cited by 7 publications

(7 citation statements)

References 30 publications

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“…If computational time is a concern, we may use the nonoverlapping subsamples. However, its statistical efficiency is reduced; see, for example, Alexopoulos, Goldsman and Wilson (2011). On the other hand, if the overlapping subsamples are used, the estimators v and v are asymptotically equivalent in the following sense.…”

Section: A General Framework For Variance Estimationmentioning

confidence: 99%

“…} is the well-known overlapping batch means (OBM) estimator (Chen and Schmeiser (2013)). Besides, Carlstein (1986) and Alexopoulos, Goldsman and Wilson (2011) studied the nonoverlapping and partially overlapping subsamples, however, these schemes are suboptimal in terms of MSE. EXAMPLE 2.4 (General case: m = 1, h → ∞).…”

Section: Example 22 (Serially Uncorrelated Casementioning

confidence: 99%

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Optimal difference-based variance estimators in time series: A general framework

Chan

2022

Ann. Statist.

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Variance estimation is important for statistical inference. It becomes nontrivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or suboptimally handle these nuisance structures. This paper develops a general framework for the estimation of the long-run variance for time series with nonconstant means. The building blocks are difference statistics. The proposed class of estimators is general enough to cover many existing estimators. Necessary and sufficient conditions for consistency are investigated. The first asymptotically optimal estimator is derived. Our proposed estimator is theoretically proven to be invariant to arbitrary mean structures, which may include trends and a possibly divergent number of discontinuities.

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Section: A General Framework For Variance Estimationmentioning

confidence: 99%

Section: Example 22 (Serially Uncorrelated Casementioning

confidence: 99%

Optimal difference-based variance estimators in time series: A general framework

Chan

2022

Ann. Statist.

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“…If computational time is a concern, we may use the nonoverlapping subsamples. However, its statistical efficiency is reduced; see, e.g., Alexopoulos, Goldsman and Wilson (2011). On the other hand, if the overlapping subsamples are used, the estimators v and v are asymptotically equivalent in the following sense.…”

Section: 2mentioning

confidence: 99%

“…is the well-known overlapping batch means (OBM) estimator (Meketon and Schmeiser, 1984). Besides, Carlstein (1986) and Alexopoulos, Goldsman and Wilson (2011) studied the non-overlapping and partially overlapping subsamples, however, these schemes are suboptimal in terms of MSE. EXAMPLE 2.4 (General case: m = 1, h → ∞).…”

Section: Example 22 (Serially Uncorrelated Casementioning

confidence: 99%

Optimal Difference-based Variance Estimators in Time Series: A General Framework

Chan¹

2021

Preprint

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Variance estimation is important for statistical inference. It becomes non-trivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or suboptimally handle these nuisance structures. This paper develops a general framework for the estimation of the long-run variance for time series with non-constant means. The building blocks are difference statistics. The proposed class of estimators is general enough to cover many existing estimators. Necessary and sufficient conditions for consistency are investigated. The first asymptotically optimal estimator is derived. Our proposed estimator is theoretically proven to be invariant to arbitrary mean structures, which may include trends and a possibly divergent number of discontinuities.k∈Z γ k is a sum of infinitely many unknowns, where γ k = E(Z 0 Z k ) is the autocovariance function (ACVF). So, estimation of v is hard. Without the nuisance structure 1 above,

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“…Asymptotic properties of the OBM estimator are studied by Alexopoulos & Goldsman () and Damerdji (), while that of the NBM estimator are studied by Chien et al () and Steiger & Wilson (). It is shown that the OBM estimator is more efficient than the NBM and partially overlapping batch means estimators in terms of MSE (Alexopoulos et al ()).…”

Section: Introductionmentioning

confidence: 99%

High‐order Corrected Estimator of Asymptotic Variance with Optimal Bandwidth

Chan

Yau

2017

Scandinavian J Statistics

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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 optimal L 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.

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Overlapping Batch Means: Something more for Nothing?

Cited by 7 publications

References 30 publications

Optimal difference-based variance estimators in time series: A general framework

Optimal difference-based variance estimators in time series: A general framework

Optimal Difference-based Variance Estimators in Time Series: A General Framework

High‐order Corrected Estimator of Asymptotic Variance with Optimal Bandwidth

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