LINEARITY OF REGRESSION FOR NON-ADJACENT WEAK RECORDS

Abstract: A complete characterization of the family of distributions with linearity of regression for future non-adjacent weak records with spacing equal to two is given. Also, in the adjacent case, weak-record versions of some known characterization results for regular records are presented

Gaussian conditional structure of the second order and the Kagan classification of multivariate distributions

The only Kagan-n,2(loc) probability measure with Gaussian conditional structure of the second order (GCS2) is a multivariate normal distribution. Also a short review of the known results on the GCS2 distributions is given.Kagan class Gaussian conditional structure of the second order multivariate normal law linearity of regression homoscedasticity characterization

Limit theorems for random permanents with exchangeable structure

Abstract Permanents of random matrices extend the concept of U-statistics with product kernels. In this paper, we study limiting behavior of permanents of random matrices with independent columns of exchangeable components. Our main results provide a general framework which unifies already existing asymptotic theory for projection matrices as well as matrices of all-iid entries. The method of the proofs is based on a Hoeffding-type orthogonal decomposition of a random permanent function. The decomposition allows us to relate asymptotic behavior of permanents to that of elementary symmetric polynomials based on triangular arrays of rowwise independent rv's. r 2004 Elsevier Inc. All rights reserved

Projection formulas for orthogonal polynomials. arxiv.org/abs/math.CA/0606092

Abstract We prove a new projection formula for the four-parameter family of orthogonal polynomials outside of the Askey-Wilson class. By carefully analyzing the recurrence relations we manage to overcome the lack of explicit expression for the orthogonality measure