TESTING THE MEANS OF INDEPENDENT NORMAL RANDOM-VARIABLES

Suppose one has available Z1, ..., Z(M) which are independent and Z(i) approximately N(mu(i), sigma(i)2) where sigma(i)2 is known. It is desired to test H-0:mu(i) = mu0, i = 1, ..., M. versus H(a):mu(i) not-equal mu0 for some i, where mu0 is a known value. Such problems arise in nonparametric component analyses and in time series analysis. A new test, the subset chi-square test method (SCSM), is proposed for this framework. The method examines the sums of squares of all subsets of the normalized random variables. The test is easily calculated and produces a criterion, similar in spirit to Akaike's (1974) AIC, which indicates the means judged to differ from mu0. This new test is found to compare favorably to existing methods in terms of power.