Quantile estimation in dependent sequences
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Authors
Heidelberger, P.
Lewis, Peter A. W.
Subjects
Quantile
quantile estimation
dependent sequences
nonparametric quantile estimators
^-mixing process
maximum transformation
extreme quantile
confidence interval estimates; averaged group quantiles
nested group quantiles.
quantile estimation
dependent sequences
nonparametric quantile estimators
^-mixing process
maximum transformation
extreme quantile
confidence interval estimates; averaged group quantiles
nested group quantiles.
Advisors
Date of Issue
1981-09
Date
Publisher
Monterey, CA; Naval Postgraduate School
Language
Abstract
Standard nonparametric estimators of quantiles based on order statistics can be used not only when the data are i.i.d., but also when the data are from a stationary, phi-mixing process of continuous random variables. However, when the random variables are highly positively correlated, sample sizes needed for acceptable precision in estimates of extreme quantiles are computationally unmanageable. A practical scheme is given, based on a maximum transformation in a two-way layout of the data, which reduces the sample size sufficiently to allow an experimenter to obtain a point estimate of an extreme quantile. Three schemes are then given which lead to confidence interval estimates for the quantile. One uses a spectral analysis of the reduced sample. The other two, averaged group quantiles and nested group quantiles, are extensions of the method of batched means to quantile estimation. None of the schemes requires that the process being simulated is regenerative
Type
Technical Report
Description
Series/Report No
Department
Organization
Identifiers
NPS Report Number
NPS-55-81-015
Sponsors
Prepared for: Chief of Naval Research
Arlington, VA
Funding
N0001481WR10001
Format
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.