Abstract
In this paper Pitman's asymptotic efficiencies (AE) as well as Kallenberg's intermediate AE of the goodness-of-fit tests based on higher-order non-overlapping spacings is considered. We study log statistic as well as entropy type statistic based on k-spacings when k may tend to infinity as n approaches infinity. It certainly compliments the available results for fixed k and provides more general result. We show that both types of statistics based on higher ordered spacings have higher efficiencies in Pitman's sense compared to their counterparts based on simple spacings. It is also shown that the Kallenberg's intermediate AE of such test coincides with its Pitman's AE, the power of the tests are also discussed.
Highlights
Consider a population with continuous cumulative distribution function G and probability density function g .We select an increasing order sample Z1' Z ' 2Z' n−1 from this population
For the first time the asymptotic normality of the statistics based on disjoint k-spacings was discussed by Del Pino,1979) and has shown that it is more efficient in Pitman sense than simple spacings statistics
That logarithms tests based on higher ordered spacings has higher efficiency in Pitman sense compared to their counterparts based on simple spacings, the (Kallenberg, 1983) intermediate efficiency of statistics (4) is discussed, the power of the tests is studied
Summary
By doing so the support of G is reduced to [0,1] and the known cumulative distribution function reduces to that of a uniform random variable on [0,1]. It is, the problem of testing the null hypothesis. Against alternative that g is probability density function of some non-uniform random variable having support on [0,1]. One way of testing the goodness-of-fit problem is based on observed frequencies which perform better in detecting differences between the distribution functions. The second type of tests is based on spacings and they are useful to detect differences between the corresponding densities. We are testing hypothesis (1) against the sequence of alternatives
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