A general approach for developing distribution free tests for general linear models based on simplicial depth is presented. In most relevant cases, the test statistic is a degenerated U-statistic so that the spectral decomposition of the conditional expectation of the kernel function is needed to derive the asymptotic distribution. A general formula for this conditional expectation is derived. ...

An analytic expression of conditional expectation of transient gamete frequency, given that one of the two loci remains polymorphic, is obtained in terms of the diffusion process by calculating the moments of the distribution. Using this expression, a model where linkage disequilibrium is introduced by a single mutation is considered. The conditional expectation of the gamete frequency given th...

We study the operator-valued free Fisher information of random matrices in an operator-valued noncommutative probability space. We obtain a formula for Φ M2(B) (A,A,M2(B), η), where A ∈ M2(B) is a 2 × 2 operator matrix on B, and η is linear operators on M2(B). Then we consider a special setting: A is an operator-valued semicircular matrix with conditional expectation covariance, and find that Φ...

Abstract In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved varying measures vaguely convergent.