TY - BOOK
T1 - Power gain by pre-testing?
AU - Albers, W.
AU - Boon, P.C.
AU - Kallenberg, W.C.M.
PY - 1999
Y1 - 1999
N2 - The aim of this paper is to study whether it is possible to gain power by pretesting,and to give insight in when this occurs, to what extent and at whichprice. A pre-test procedure consists of a preliminary test which tests a particularproperty of a given restricted model, followed by a main test for the mainhypothesis regarding the parameter of interest. After acceptance by the preliminarytest, a basic main test is used in the restricted model. After rejection bythe preliminary test, a more general main test is used which does not use priorinformation about the underlying distribution. The procedure is analyzed in themodel against which the preliminary test protects. For classes of tests includingthe standard rst-order optimal tests, a transparent expression is given for thepower and size dierence of the pre-test procedure compared to the power and(correct) size of the second main test. This expression is based on second-orderasymptotics and gives qualitative and quantitative insight in the behavior of theprocedure. It shows that substantial power gain, not merely due to size violation,is possible if the second main test really diers from the basic main test. Thesmaller 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 pretesting,and to give insight in when this occurs, to what extent and at whichprice. A pre-test procedure consists of a preliminary test which tests a particularproperty of a given restricted model, followed by a main test for the mainhypothesis regarding the parameter of interest. After acceptance by the preliminarytest, a basic main test is used in the restricted model. After rejection bythe preliminary test, a more general main test is used which does not use priorinformation about the underlying distribution. The procedure is analyzed in themodel against which the preliminary test protects. For classes of tests includingthe standard rst-order optimal tests, a transparent expression is given for thepower and size dierence of the pre-test procedure compared to the power and(correct) size of the second main test. This expression is based on second-orderasymptotics and gives qualitative and quantitative insight in the behavior of theprocedure. It shows that substantial power gain, not merely due to size violation,is possible if the second main test really diers from the basic main test. Thesmaller the correlation between the two main tests, the larger the power gain.
KW - MSC-62E20
KW - MSC-62F05
KW - Pre-test procedure
KW - Power gain
KW - Robustness of validity
KW - Second-order asymtotics
M3 - Report
T3 - Memorandum
BT - Power gain by pre-testing?
PB - University of Twente, Department of Applied Mathematics
CY - Enschede
ER -