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On the Likelihood Ratio Test for a Shift in Location of Normal Populations

K. J. Worsley
Journal of the American Statistical Association
Vol. 74, No. 366 (Jun., 1979), pp. 365-367
DOI: 10.2307/2286336
Stable URL: http://www.jstor.org/stable/2286336
Page Count: 3
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On the Likelihood Ratio Test for a Shift in Location of Normal Populations
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Abstract

An alternative to the hypothesis that the sequence X1, ..., Xn are independent and identically distributed normal random variables, with mean μ and variance σ2, is that the location parameter μ shifts at some unknown instant. The null distributions of likelihood ratio test statistics are given by Hawkins (1977) for the two cases of known and unknown σ2. Unfortunately, the null distribution for unknown σ2 obtained in that article is incorrect. In this article the correct null distribution is found and a numerical integration technique is used to obtain standard percentage points for n = 3(1)10. A Monte Carlo method is used to obtain additional standard percentage points for n = 15(5)50.

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