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We propose two families of scale-free exponentiality tests based on the recent characterization of exponentiality by Arnold and Villasenor. The test statistics are based on suitable functionals of U-empirical distribution functions. The family of integral statistics can be reduced to V- or U-statistics with relatively simple non-degenerate kernels. They are asymptotically normal and have reasonably high local Bahadur efficiency under common alternatives. This efficiency is compared with simulated powers of new tests. On the other hand, the Kolmogorov type tests demonstrate very low local Bahadur efficiency and rather moderate power for common alternatives,and can hardly be recommended to practitioners. We also explore the conditions of local asymptotic optimality of new tests and describe for both families special most favorable alternatives for which the tests are fully efficient.
We generate all the Orthogonal Arrays (OAs) of a given size n and strength t as the union of a collection of OAs which belong to an inclusion-minimal set of OAs. We derive a formula for computing the (Generalized) Word Length Pattern of a union of OA
Over the last two decades, many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool. Can the discoveries from these data mining approaches be spurious
The treatment effects of the same therapy observed from multiple clinical trials can often be very different. Yet the patient characteristics accounting for these differences may not be identifiable in real world practice. There needs to be an unbias
Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order moment assumpti
The aim of online monitoring is to issue an alarm as soon as there is significant evidence in the collected observations to suggest that the underlying data generating mechanism has changed. This work is concerned with open-end, nonparametric procedu