The Annals of Statistics

Optimal Goodness-of-Fit Tests for Location/Scale Families of Distributions Based on the Sum of Squares of $L$-Statistics

Abstract

A class of goodness-of-fit tests based on sums of squares of $L$-statistics is proposed for testing a composite parametric location and/or scale null hypothesis versus a general parametric alternative. It is shown that such tests can be constructed optimally to have the same asymptotic power against sequences of local alternatives as the generalized likelihood ratio statistics [G.L.R.S.] and, in fact, under suitable regularity conditions to be asymptotically equivalent to the G.L.R.S. One advantage of the proposed test statistic over the G.L.R.S. is that only an estimate of the scale parameter is needed in the computation of the statistic. No other parameter estimates are required. Also, an example of the practical implementation of the proposed hypothesis testing procedure is given.

Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 315-330.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346595

Digital Object Identifier
doi:10.1214/aos/1176346595

Mathematical Reviews number (MathSciNet)
MR773170

Zentralblatt MATH identifier
0576.62031

JSTOR
LaRiccia, Vincent N.; Mason, David M. Optimal Goodness-of-Fit Tests for Location/Scale Families of Distributions Based on the Sum of Squares of $L$-Statistics. Ann. Statist. 13 (1985), no. 1, 315--330. doi:10.1214/aos/1176346595. https://projecteuclid.org/euclid.aos/1176346595