Combining independent onesample tests of significance
 Madan L. Puri
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The problem of combining independent onesample tests of significance is considered using techniques developed by the author (1965). LetX _{i1},..., X_{im} _{i} be positive observations andY _{i1},..., Y_{in} _{i}, the absolute values of negative observations in a sampleZ _{i1},..., Z_{iN} _{i} ofN _{i}=m_{i}+n_{i} independent and identically distributed random variables from a population with continuous cumulative distribution function \(\Pi _{0_i } (z);i = 1, \cdots ,k\) .
Then for testing the hypothesis that each of the distributions \(\Pi _{0_i } (z)\) is symmetric with respect to the origin, linear combinations of several onesample test statistics are considered. Under suitable assumptions, two sets of combination coefficients are derived. One of them yields a class of tests with a region of consistency that is independent of the proportion of sample sizes (designfree tests) and the other has asymptotically the maximum power (locally asymptotically most powerful tests). Finally, these tests are compared with respect to the asymptotic values of their power against Pitman's shift alternatives and Lehmann's distribution free alternatives.
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 Title
 Combining independent onesample tests of significance
 Journal

Annals of the Institute of Statistical Mathematics
Volume 19, Issue 1 , pp 285300
 Cover Date
 19671201
 DOI
 10.1007/BF02911681
 Print ISSN
 00203157
 Online ISSN
 15729052
 Publisher
 SpringerVerlag
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 Authors

 Madan L. Puri ^{(1)}
 Author Affiliations

 1. Courant Institute of Mathematical Sciences, New York University, New York, USA