EXTREME-VALUE MOMENT GOODNESS-OF-FIT TESTS

THEODORE P. HILL^{1} AND VICTOR PEREZ-ABREU

1School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, U.S.A.,

e-mail: hill@math.gatech.edu 2Centro de Investigacíon en Matemáticas, Guanajuato, Gto 36000, Mexico, e-mail: pabreu@fractal.cimat.mx

(Received April 28, 1998; revised February 25, 2000)

Abstract. A general goodness-of-fit test for scale-parameter families of distributions is introduced, which is based on quotients of expected sample minima. The test is independent of the mean of the distribution, and, in applications to testing for exponentiality of data, compares favorably to other goodness-of-fit tests for exponentiality based on the empirical distribution function, regression methods and correlation statistics. The new minimal-moment method uses ratios of easily-calculated, unbiased, strongly consistent U-statistics, and the general technique can be used to test many standard composite null hypotheses such as exponentiality, normality or uniformity (as well as simple null hypotheses).

Key words and phrases: Goodness-of-fit, scale-parameter families, U-statistics, exponential family, composite exponential hypothesis, minimal moments, extreme values.