Journal of the Royal Statistical Society. Series B (Methodological)
Выпуски:
Опубликовано на портале: 06-04-2004
Sandor Csorgo, Julian Faraway
Journal of the Royal Statistical Society. Series B (Methodological).
1996.
Vol. 58.
No. 1.
It is shown that an asymptotically precise one-term correction to the asymptotic
distribution function of the classical Cramйr-von Mises statistic approximates the
exact distribution function remarkably closely for sample sizes as small as 7 or
even smaller. This correction can be quickly evaluated, and hence it is suitable
for the computation of practically exact p-values when testing simple goodness of
fit.
Abstract2
It is shown that an asymptotically precise one-term correction to the asymptotic
distribution function of the classical Cramer-von Mises statistic approximates the
exact distribution function remarkably closely for sample sizes as small as 7 or
even smaller. This correction can be quickly evaluated, and hence it is suitable
for the computation of practically exact $p$-values when testing simple goodness
of fit. Similar findings hold for Watson's rotationally invariant modification, where
a sample size of 4 appears to suffice.
