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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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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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container_title	Biometrika
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creator	GOFFINET, BRUNO WALLACH, DANIEL
description	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.
doi_str_mv	10.1093/biomet/83.4.791
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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. 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An example in genetics is given.</description><subject>Approximation</subject><subject>Chromosomes</subject><subject>Distribution theory</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>Importance sampling Mixture model</subject><subject>Life Sciences</subject><subject>Mathematics</subject><subject>Monte Carlo</subject><subject>Population estimates</subject><subject>Probability and statistics</subject><subject>QTL</subject><subject>Quantile estimation</subject><subject>Quantitative trait loci</subject><subject>Ratio test</subject><subject>Sampling distributions</subject><subject>Sampling theory, sample surveys</subject><subject>Sciences and techniques of general use</subject><subject>Simulation</subject><subject>Statistical variance</subject><subject>Statistics</subject><subject>Unbiased estimators</subject><issn>0006-3444</issn><issn>1464-3510</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1996</creationdate><recordtype>article</recordtype><recordid>eNpFjz1PwzAQhi0EEqUwszBkYGFIa8ffY1VRglRUBpAQi-UkF-qSL2KD4N-TKqhMp7vnuTu9CF0SPCNY03nm2hrCXNEZm0lNjtCEMMFiygk-RhOMsYgpY-wUnXm_27eCiwkimy642nkoIld3bR9sk0Pkbd1VrnmLPj5tE1wFEfhBs8G1zTk6KW3l4eKvTtHz6vZpmcbrzd39crGOt4nkIZZZwpiQYBUIQoDQUmpQNsupKIXCoGieYaUTSAooJWheWFIqnheCacWJoFN0M97d2sp0_fC9_zGtdSZdrM1-hhOhhGbyiwzu9eh21ue2KvshhfOHrURRRcVeuxq1nQ9t_48plYMy4HjEzgf4PmDbvxshqeQmfXk1j5o9PCzTleH0F3bMbk8</recordid><startdate>19961201</startdate><enddate>19961201</enddate><creator>GOFFINET, BRUNO</creator><creator>WALLACH, DANIEL</creator><general>Oxford University Press</general><general>Biometrika Trust</general><general>Oxford University Press (OUP)</general><scope>BSCLL</scope><scope>IQODW</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0003-3500-8179</orcidid></search><sort><creationdate>19961201</creationdate><title>Optimised importance sampling quantile estimation</title><author>GOFFINET, BRUNO ; WALLACH, DANIEL</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-h275t-7b24467ea8e611e13f79e8abc36f680e83cb0892e2def7e95da1f85cd64985163</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1996</creationdate><topic>Approximation</topic><topic>Chromosomes</topic><topic>Distribution theory</topic><topic>Estimators</topic><topic>Exact sciences and technology</topic><topic>Importance sampling Mixture model</topic><topic>Life Sciences</topic><topic>Mathematics</topic><topic>Monte Carlo</topic><topic>Population estimates</topic><topic>Probability and statistics</topic><topic>QTL</topic><topic>Quantile estimation</topic><topic>Quantitative trait loci</topic><topic>Ratio test</topic><topic>Sampling distributions</topic><topic>Sampling theory, sample surveys</topic><topic>Sciences and techniques of general use</topic><topic>Simulation</topic><topic>Statistical variance</topic><topic>Statistics</topic><topic>Unbiased estimators</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>GOFFINET, BRUNO</creatorcontrib><creatorcontrib>WALLACH, DANIEL</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Biometrika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>GOFFINET, BRUNO</au><au>WALLACH, DANIEL</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimised importance sampling quantile estimation</atitle><jtitle>Biometrika</jtitle><date>1996-12-01</date><risdate>1996</risdate><volume>83</volume><issue>4</issue><spage>791</spage><epage>800</epage><pages>791-800</pages><issn>0006-3444</issn><eissn>1464-3510</eissn><coden>BIOKAX</coden><abstract>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. 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language	eng
recordid	cdi_hal_primary_oai_HAL_hal_02686947v1
source	Oxford Journals Online; JSTOR Archival Journals
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
title	Optimised importance sampling quantile estimation
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