EMPIRICALLY ACCELERATED CONVERGENCE OF THE SPACINGS STATISTICS TO NORMALITY

If the asymptotic normality of a statistic is inadequate for approximating its distribution in practice, then the statistic may be transformed in order to improve the approximation by accelerating the convergence to normality. We treat a goodness-of-fit statistic, the sum of the logarithms of generalized uniform spacings introduced by Cressie (1976, 1978), in this spirit. Specifically, we apply the method of maximum likelihood to simulations of the statistic in order to estimate a power transformation, as in Box & Cox (1964), and hence develop a small sample normal approximation. This approximation provides a more versatile method of applying the statistic than currently available tables of percentiles.