Power gain by pre-testing?

Willem/Wim Albers, P.C. Boon, W.C.M. Kallenberg

Research output: Book/ReportReportOther research output

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Abstract

The aim of this paper is to study whether it is possible to gain power by pre-testing, and to give insight in when this occurs, to what extent, and, at which price. A pre-test procedure consists of a preliminary test which tests a particular property of a given restricted model, followed by a main test for the main hypothesis regarding the parameter of interest. After acceptance by the preliminary test, a basic main test is used in the restricted model. After rejection by the preliminary test, a more general main test is used which does not use prior information about the underlying distribution. The procedure is analyzed in the model against which the preliminary test protects. For classes of tests including the standard first-order optimal tests, a transparent expression is given for the power and size difference of the pre-test procedure compared to the power and (correct) size of the second main test. This expression is based on second-order asymptotics and gives qualitative and quantitative insight in the behaviour of the procedure. It shows that substantial power gain, not merely due to size violation, is possible if the second main test really differs from the basic main test. The smaller the correlation between the two main tests, the larger the power gain.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Publication statusPublished - 1999

Publication series

Name
PublisherDepartment of Applied Mathematics, University of Twente
No.1488
ISSN (Print)0169-2690

Keywords

  • MSC-62E20
  • EWI-3308
  • IR-65677
  • MSC-62F05

Cite this

Albers, WW., Boon, P. C., & Kallenberg, W. C. M. (1999). Power gain by pre-testing? Enschede: University of Twente, Department of Applied Mathematics.
Albers, Willem/Wim ; Boon, P.C. ; Kallenberg, W.C.M. / Power gain by pre-testing?. Enschede : University of Twente, Department of Applied Mathematics, 1999.
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abstract = "The aim of this paper is to study whether it is possible to gain power by pre-testing, and to give insight in when this occurs, to what extent, and, at which price. A pre-test procedure consists of a preliminary test which tests a particular property of a given restricted model, followed by a main test for the main hypothesis regarding the parameter of interest. After acceptance by the preliminary test, a basic main test is used in the restricted model. After rejection by the preliminary test, a more general main test is used which does not use prior information about the underlying distribution. The procedure is analyzed in the model against which the preliminary test protects. For classes of tests including the standard first-order optimal tests, a transparent expression is given for the power and size difference of the pre-test procedure compared to the power and (correct) size of the second main test. This expression is based on second-order asymptotics and gives qualitative and quantitative insight in the behaviour of the procedure. It shows that substantial power gain, not merely due to size violation, is possible if the second main test really differs from the basic main test. The smaller the correlation between the two main tests, the larger the power gain.",
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author = "Willem/Wim Albers and P.C. Boon and W.C.M. Kallenberg",
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publisher = "University of Twente, Department of Applied Mathematics",
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Albers, WW, Boon, PC & Kallenberg, WCM 1999, Power gain by pre-testing? University of Twente, Department of Applied Mathematics, Enschede.

Power gain by pre-testing? / Albers, Willem/Wim; Boon, P.C.; Kallenberg, W.C.M.

Enschede : University of Twente, Department of Applied Mathematics, 1999.

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Power gain by pre-testing?

AU - Albers, Willem/Wim

AU - Boon, P.C.

AU - Kallenberg, W.C.M.

N1 - Imported from MEMORANDA

PY - 1999

Y1 - 1999

N2 - The aim of this paper is to study whether it is possible to gain power by pre-testing, and to give insight in when this occurs, to what extent, and, at which price. A pre-test procedure consists of a preliminary test which tests a particular property of a given restricted model, followed by a main test for the main hypothesis regarding the parameter of interest. After acceptance by the preliminary test, a basic main test is used in the restricted model. After rejection by the preliminary test, a more general main test is used which does not use prior information about the underlying distribution. The procedure is analyzed in the model against which the preliminary test protects. For classes of tests including the standard first-order optimal tests, a transparent expression is given for the power and size difference of the pre-test procedure compared to the power and (correct) size of the second main test. This expression is based on second-order asymptotics and gives qualitative and quantitative insight in the behaviour of the procedure. It shows that substantial power gain, not merely due to size violation, is possible if the second main test really differs from the basic main test. The smaller the correlation between the two main tests, the larger the power gain.

AB - The aim of this paper is to study whether it is possible to gain power by pre-testing, and to give insight in when this occurs, to what extent, and, at which price. A pre-test procedure consists of a preliminary test which tests a particular property of a given restricted model, followed by a main test for the main hypothesis regarding the parameter of interest. After acceptance by the preliminary test, a basic main test is used in the restricted model. After rejection by the preliminary test, a more general main test is used which does not use prior information about the underlying distribution. The procedure is analyzed in the model against which the preliminary test protects. For classes of tests including the standard first-order optimal tests, a transparent expression is given for the power and size difference of the pre-test procedure compared to the power and (correct) size of the second main test. This expression is based on second-order asymptotics and gives qualitative and quantitative insight in the behaviour of the procedure. It shows that substantial power gain, not merely due to size violation, is possible if the second main test really differs from the basic main test. The smaller the correlation between the two main tests, the larger the power gain.

KW - MSC-62E20

KW - EWI-3308

KW - IR-65677

KW - MSC-62F05

M3 - Report

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Albers WW, Boon PC, Kallenberg WCM. Power gain by pre-testing? Enschede: University of Twente, Department of Applied Mathematics, 1999.