Fast Estimators of the Jackknife
The jackknife is a reliable method for estimating standard error nonparametrically. The method is easy to use, but is computationally intensive. The time required to compute the jackknife standard error for an estimator will depend on the time required to compute itself. For some estimators the requ...
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description | The jackknife is a reliable method for estimating standard error nonparametrically. The method is easy to use, but is computationally intensive. The time required to compute the jackknife standard error for an estimator
will depend on the time required to compute
itself. For some estimators the required time is prohibitive. This may be especially true in simulation studies where
and its standard error are computed for a large number of datasets.
Let X
1
, X
2
, ..., X
N
be a random sample and
the estimator computed with X
i
removed. Then
is the jackknife estimator of the variability of
where
. In this paper estimators of
are defined that can be computed quickly while sacrificing little precision or accuracy. The method requires that random variables
are available that can be computed quickly and are strongly correlated with
. It is described how
can generally be obtained, and the method is illustrated with two examples. The paper focuses on the jackknife estimator for standard error, but the method can also be applied to quickly compute the jackknife estimator of bias. |
doi_str_mv | 10.1080/00031305.1997.10473969 |
format | Article |
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will depend on the time required to compute
itself. For some estimators the required time is prohibitive. This may be especially true in simulation studies where
and its standard error are computed for a large number of datasets.
Let X
1
, X
2
, ..., X
N
be a random sample and
the estimator computed with X
i
removed. Then
is the jackknife estimator of the variability of
where
. In this paper estimators of
are defined that can be computed quickly while sacrificing little precision or accuracy. The method requires that random variables
are available that can be computed quickly and are strongly correlated with
. It is described how
can generally be obtained, and the method is illustrated with two examples. The paper focuses on the jackknife estimator for standard error, but the method can also be applied to quickly compute the jackknife estimator of bias.</description><identifier>ISSN: 0003-1305</identifier><identifier>EISSN: 1537-2731</identifier><identifier>DOI: 10.1080/00031305.1997.10473969</identifier><identifier>CODEN: ASTAAJ</identifier><language>eng</language><publisher>Alexandria, VA: Taylor & Francis Group</publisher><subject>Approximation ; Bootstrap ; Cost estimates ; Datasets ; Estimate reliability ; Estimation bias ; Estimation methods ; Estimators ; Exact sciences and technology ; Influence curve ; Mathematics ; Measurement error ; Nonparametric inference ; Probability and statistics ; Random sampling ; Sampling ; Sampling theory, sample surveys ; Sciences and techniques of general use ; Standard error ; Statistical variance ; Statistics</subject><ispartof>The American statistician, 1997-08, Vol.51 (3), p.235-240</ispartof><rights>Copyright Taylor & Francis Group, LLC 1997</rights><rights>Copyright 1997 American Statistical Association</rights><rights>1997 INIST-CNRS</rights><rights>Copyright American Statistical Association Aug 1997</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c339t-b0f7b8c1dca5c31daad1dcbe7a31029a61e315094075d37816e7de591468b1dc3</citedby><cites>FETCH-LOGICAL-c339t-b0f7b8c1dca5c31daad1dcbe7a31029a61e315094075d37816e7de591468b1dc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2684894$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2684894$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,27846,27901,27902,57992,57996,58225,58229</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=2815921$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Buzas, J. S.</creatorcontrib><title>Fast Estimators of the Jackknife</title><title>The American statistician</title><description>The jackknife is a reliable method for estimating standard error nonparametrically. The method is easy to use, but is computationally intensive. The time required to compute the jackknife standard error for an estimator
will depend on the time required to compute
itself. For some estimators the required time is prohibitive. This may be especially true in simulation studies where
and its standard error are computed for a large number of datasets.
Let X
1
, X
2
, ..., X
N
be a random sample and
the estimator computed with X
i
removed. Then
is the jackknife estimator of the variability of
where
. In this paper estimators of
are defined that can be computed quickly while sacrificing little precision or accuracy. The method requires that random variables
are available that can be computed quickly and are strongly correlated with
. It is described how
can generally be obtained, and the method is illustrated with two examples. The paper focuses on the jackknife estimator for standard error, but the method can also be applied to quickly compute the jackknife estimator of bias.</description><subject>Approximation</subject><subject>Bootstrap</subject><subject>Cost estimates</subject><subject>Datasets</subject><subject>Estimate reliability</subject><subject>Estimation bias</subject><subject>Estimation methods</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>Influence curve</subject><subject>Mathematics</subject><subject>Measurement error</subject><subject>Nonparametric inference</subject><subject>Probability and statistics</subject><subject>Random sampling</subject><subject>Sampling</subject><subject>Sampling theory, sample surveys</subject><subject>Sciences and techniques of general use</subject><subject>Standard error</subject><subject>Statistical variance</subject><subject>Statistics</subject><issn>0003-1305</issn><issn>1537-2731</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1997</creationdate><recordtype>article</recordtype><sourceid>K30</sourceid><sourceid>8G5</sourceid><sourceid>BEC</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNqFkE1LAzEQhoMoWKt_QRb1ujWTbL6OpbR-UPCi55DNZnHbbVOTLdJ_b5a26kU8ZRKeeSfzIHQNeARY4nuMMQWK2QiUEumpEFRxdYIGwKjIiaBwigY9lPfUObqIcZGuWHAyQNnMxC6bxq5Zmc6HmPk6695d9mzscrluaneJzmrTRnd1OIfobTZ9nTzm85eHp8l4nltKVZeXuBaltFBZwyyFypgq1aUThgImynBwFBhWBRasokICd6JyTEHBZZlIOkQ3-9xN8B9bFzu98NuwTiM1IbIQIKVM0O1fEAiGJWWS80TxPWWDjzG4Wm9CWi_sNGDdK9NHZbpXpo_KUuPdId5Ea9o6mLVt4nc3kcAUgR9sEZOy3-GEYqEJl4VURcLGe6xZ1z6szKcPbaU7s2t9OEbTf370BaBxh6o</recordid><startdate>19970801</startdate><enddate>19970801</enddate><creator>Buzas, J. 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S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c339t-b0f7b8c1dca5c31daad1dcbe7a31029a61e315094075d37816e7de591468b1dc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1997</creationdate><topic>Approximation</topic><topic>Bootstrap</topic><topic>Cost estimates</topic><topic>Datasets</topic><topic>Estimate reliability</topic><topic>Estimation bias</topic><topic>Estimation methods</topic><topic>Estimators</topic><topic>Exact sciences and technology</topic><topic>Influence curve</topic><topic>Mathematics</topic><topic>Measurement error</topic><topic>Nonparametric inference</topic><topic>Probability and statistics</topic><topic>Random sampling</topic><topic>Sampling</topic><topic>Sampling theory, sample surveys</topic><topic>Sciences and techniques of general use</topic><topic>Standard error</topic><topic>Statistical variance</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Buzas, J. 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S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fast Estimators of the Jackknife</atitle><jtitle>The American statistician</jtitle><date>1997-08-01</date><risdate>1997</risdate><volume>51</volume><issue>3</issue><spage>235</spage><epage>240</epage><pages>235-240</pages><issn>0003-1305</issn><eissn>1537-2731</eissn><coden>ASTAAJ</coden><abstract>The jackknife is a reliable method for estimating standard error nonparametrically. The method is easy to use, but is computationally intensive. The time required to compute the jackknife standard error for an estimator
will depend on the time required to compute
itself. For some estimators the required time is prohibitive. This may be especially true in simulation studies where
and its standard error are computed for a large number of datasets.
Let X
1
, X
2
, ..., X
N
be a random sample and
the estimator computed with X
i
removed. Then
is the jackknife estimator of the variability of
where
. In this paper estimators of
are defined that can be computed quickly while sacrificing little precision or accuracy. The method requires that random variables
are available that can be computed quickly and are strongly correlated with
. It is described how
can generally be obtained, and the method is illustrated with two examples. The paper focuses on the jackknife estimator for standard error, but the method can also be applied to quickly compute the jackknife estimator of bias.</abstract><cop>Alexandria, VA</cop><pub>Taylor & Francis Group</pub><doi>10.1080/00031305.1997.10473969</doi><tpages>6</tpages></addata></record> |
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language | eng |
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source | Jstor Complete Legacy; Periodicals Index Online; JSTOR Mathematics & Statistics |
subjects | Approximation Bootstrap Cost estimates Datasets Estimate reliability Estimation bias Estimation methods Estimators Exact sciences and technology Influence curve Mathematics Measurement error Nonparametric inference Probability and statistics Random sampling Sampling Sampling theory, sample surveys Sciences and techniques of general use Standard error Statistical variance Statistics |
title | Fast Estimators of the Jackknife |
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