Optimised importance sampling quantile estimation

This paper considers the use of an auxiliary variable X* to estimate quantiles of a test statistic X; X* may be an asymptotic expansion of X, or a simplified version which ignores some of the covariance structure. The proposed estimator involves three stages. First a large sample is drawn, and X* is...

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Bibliographic Details
Published in:Biometrika 1996-12, Vol.83 (4), p.791-800
Main Authors: GOFFINET, BRUNO, WALLACH, DANIEL
Format: Article
Language:English
Subjects:
Approximation
Chromosomes
Distribution theory
Estimators
Exact sciences and technology
Importance sampling Mixture model
Life Sciences
Mathematics
Monte Carlo
Population estimates
Probability and statistics
QTL
Quantile estimation
Quantitative trait loci
Ratio test
Sampling distributions
Sampling theory, sample surveys
Sciences and techniques of general use
Simulation
Statistical variance
Statistics
Unbiased estimators
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Summary:This paper considers the use of an auxiliary variable X* to estimate quantiles of a test statistic X; X* may be an asymptotic expansion of X, or a simplified version which ignores some of the covariance structure. The proposed estimator involves three stages. First a large sample is drawn, and X* is evaluated. Then a first subsample is drawn, X and X* are evaluated and the conditional distribution of X given X* is estimated. Then a second subsample is drawn with weighting which is optimised for this conditional distribution, and for a particular quantile. From this subsample, an importance sampling estimator of the quantile is obtained. The resulting estimator is shown to have substantially lower mean squared error than the conventional estimator, and to be reasonably robust both to errors in the model for the conditional distribution and to the quantile assumed for the optimisation. An example in genetics is given.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/83.4.791