Testing fit with nuisance location and scale parameters

Lionel Weiss

Naval Research Logistics Quarterly, 1975, vol. 22, issue 1, 55-63

Abstract: For each n, X1(n),…, Xn(n) are independent and identically distributed random variables, each with cumulative distribution function F(x) which is known to be absolutely continuous but is otherwise unknown. The problem is to test the hypothesis that \documentclass{article}\pagestyle{empty}\begin{document}$ F(x) = G\left( {{\textstyle{{x - \theta _1 } \over {\theta _2 }}}} \right) $\end{document}, where the cumulative distribution function Gx is completely specified and satisfies certain regularity conditions, and the parameters θ1, θ2 are unknown and unspecified, except that the scale parameter θ2, is positive. Y1 (n) ≦ Y2 (n) ≦ … ≦ Yn (n)are the ordered values of X1(n),…, Xn(n). A test based on a certain subset of {Yi(n)} is proposed, is shown to have asymptotically a normal distribution when the hypothesis is true, and is shown to be consistent against all alternatives satisfying a mild regularity condition.

Date: 1975
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:22:y:1975:i:1:p:55-63

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