Efficient computation of statistical procedures based on all subsets of a specified size

John E. Hinkle; Arnold J. Stromberg

doi:10.1080/03610929608831709

Efficient computation of statistical procedures based on all subsets of a specified size

John E. Hinkle, Arnold J. Stromberg

Dr. Bing Zhang Department of Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Many statistical techniques require that computations be done on all subsets of size r in a data set of size n. Typically, this is done lexographically, i.e., with nested for-loops. If an exchange one point update formula is available, then it is used on the inner loop. In this paper we discuss a method of counting through all subsets of size r in a data set of size n by changing only one element between successive subsets. Such methods have been studied in the applied mathematics literature but are mostly unknown to statisticians. The advantage of such methods is that an update formula can be used at every step, thus potentially saving computation time. The method used to compute the next subset in the list requires some computation time, and thus the new method will only be faster if the update formula is sufficiently faster than doing the computation from scratch.

Original language	English
Pages (from-to)	489-500
Number of pages	12
Journal	Communications in Statistics - Theory and Methods
Volume	25
Issue number	3
DOIs	https://doi.org/10.1080/03610929608831709
State	Published - 1996

Bibliographical note

Funding Information:
'John Hinkle is a Ph.D. student and Arnold Stromberg is an Assistant Professor in the Department of Statistics at the University of Kentucky, 817 Patterson Office Tower, Lexington, KY 40506-0027. Hinkle was partially supported by the College of Arts and Sciences at the University of Kentucky and initial work on this manuscript by Stromberg was supported by NSF grant DMS-9204380 and NSA grant MDA-904-92-H-3077. The authors thank Carl Brezovcc and Carl Lee for their assistance.

Funding

'John Hinkle is a Ph.D. student and Arnold Stromberg is an Assistant Professor in the Department of Statistics at the University of Kentucky, 817 Patterson Office Tower, Lexington, KY 40506-0027. Hinkle was partially supported by the College of Arts and Sciences at the University of Kentucky and initial work on this manuscript by Stromberg was supported by NSF grant DMS-9204380 and NSA grant MDA-904-92-H-3077. The authors thank Carl Brezovcc and Carl Lee for their assistance.

Funders	Funder number
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS-9204380
University of Kentucky
National Security Agency	MDA-904-92-H-3077
College of Arts and Sciences, Boston University

Keywords

Cook's distance
Distributed computing
Gray code
Jackknife

ASJC Scopus subject areas

Statistics and Probability

Access to Document

10.1080/03610929608831709

Cite this

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title = "Efficient computation of statistical procedures based on all subsets of a specified size",

abstract = "Many statistical techniques require that computations be done on all subsets of size r in a data set of size n. Typically, this is done lexographically, i.e., with nested for-loops. If an exchange one point update formula is available, then it is used on the inner loop. In this paper we discuss a method of counting through all subsets of size r in a data set of size n by changing only one element between successive subsets. Such methods have been studied in the applied mathematics literature but are mostly unknown to statisticians. The advantage of such methods is that an update formula can be used at every step, thus potentially saving computation time. The method used to compute the next subset in the list requires some computation time, and thus the new method will only be faster if the update formula is sufficiently faster than doing the computation from scratch.",

keywords = "Cook's distance, Distributed computing, Gray code, Jackknife",

author = "Hinkle, \{John E.\} and Stromberg, \{Arnold J.\}",

note = "Funding Information: 'John Hinkle is a Ph.D. student and Arnold Stromberg is an Assistant Professor in the Department of Statistics at the University of Kentucky, 817 Patterson Office Tower, Lexington, KY 40506-0027. Hinkle was partially supported by the College of Arts and Sciences at the University of Kentucky and initial work on this manuscript by Stromberg was supported by NSF grant DMS-9204380 and NSA grant MDA-904-92-H-3077. The authors thank Carl Brezovcc and Carl Lee for their assistance.",

year = "1996",

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language = "English",

volume = "25",

pages = "489--500",

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AU - Stromberg, Arnold J.

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PY - 1996

Y1 - 1996

N2 - Many statistical techniques require that computations be done on all subsets of size r in a data set of size n. Typically, this is done lexographically, i.e., with nested for-loops. If an exchange one point update formula is available, then it is used on the inner loop. In this paper we discuss a method of counting through all subsets of size r in a data set of size n by changing only one element between successive subsets. Such methods have been studied in the applied mathematics literature but are mostly unknown to statisticians. The advantage of such methods is that an update formula can be used at every step, thus potentially saving computation time. The method used to compute the next subset in the list requires some computation time, and thus the new method will only be faster if the update formula is sufficiently faster than doing the computation from scratch.

AB - Many statistical techniques require that computations be done on all subsets of size r in a data set of size n. Typically, this is done lexographically, i.e., with nested for-loops. If an exchange one point update formula is available, then it is used on the inner loop. In this paper we discuss a method of counting through all subsets of size r in a data set of size n by changing only one element between successive subsets. Such methods have been studied in the applied mathematics literature but are mostly unknown to statisticians. The advantage of such methods is that an update formula can be used at every step, thus potentially saving computation time. The method used to compute the next subset in the list requires some computation time, and thus the new method will only be faster if the update formula is sufficiently faster than doing the computation from scratch.

KW - Cook's distance

KW - Distributed computing

KW - Gray code

KW - Jackknife

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JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 3

ER -

Efficient computation of statistical procedures based on all subsets of a specified size

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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