In many practical detection and classi cation problems, the signals of interest exhibit some uncertain nuisance parameters, such as the unknown delay and Doppler in radar. For optimal performance, the form of such parameters must be known and exploited as is done in the generalized likelihood ratio test (GLRT). In practice, the statistics required for designing the GLRT processors are not avail...

In two-dimensional noncommutive space for the case of both position position and momentum momentum noncommuting, a constraint between noncommutative parameters is investigated. The related topic of guaranteeing Bose Einstein statistics in noncommutive space in the general case are elucidated: Bose Einstein statistics is guaranteed by the deformed Heisenberg Weyl algebra itself, independent of d...

In this paper, the concomitants of case-II of generalized order statistics from Farlie-Gumbel-Morgenstern (FGM) distributions and recurrence relations between their moments are studied. Further, we provide the minimum variance linear unbiased estimator of the location and scale parameters of the concomitants of ordinary order statistics from some distributions.

Tests for change-points for location or regression models are often based on cumulative sums of recursive residuals. In the context of general estimable parameters (functionals of the underlying distributions), such recursive residuals may be defined in terms of recursive U-statistics. Along with some invariance principles for recursive U-statistics, asymptotic properties of some proposed tests...

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We study the spectral statistics for quantized skew translations on the torus, which are ergodic but not mixing for irrational parameters. It is shown explicitly that in this case the level– spacing distribution and other common spectral statistics, like the number variance, do not exist in the semiclassical limit. ∗ E-mail address: [email protected] ∗∗ E-mail address: grischa.haag...