A comparison of some test statistics of the Kolmogorov type
comparisonofsome00hend.pdf (1.327Mb)Abstract
It is natural to associate optimal estimation and optimal statistical testing. In this paper
continuous function estimation of the cumulative distribution is used to define two test statistics that compete with the Kolmogorov Dn
statistic. The first statistic, Cn, is attributed to Pyke and the second, Rn, is obtained by
polygonalizing the sample distribution function. It is known that both are asymptotically equivalent to the Kolmogorov statistic. Using the methods of J. Durbin, the small sample distributions are tabled as well as the
critical points for significance levels of .20, .10 , .05 , .025 , and .01. It is shown that
is stochastically smaller than Dn and it appears that Cn is also smaller than Dn.
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