Abstract. 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.

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519.2We construct integral and supremum type tests of exponentiality based on Ahsanullah's characterization of the exponential law. We discuss limiting distributions and large deviations of new test statistics under the null-hypothesis and calculate their local Bahadur efficiency under common parametric alternatives. Conditions of local optimality of the new statistics are given. Bibliography: 33 titles.

Bifractional Brownian motion (bfBm) is a centered Gaussian process with covarianceWe study the existence of bfBm for a given pair of parameters (h, k) and encounter some related limiting processes.MSC: primary 60G15, secondary 42A82.

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