.On a generalization of the classical random sampling scheme and unbiased estimation, by Ya.Lumelskii, V.Voinov, M.Nikulin and P.Fegin

Yan Lumelskii , Vassily Voinov , Mikhail Nikulin (1) , Paul Paul Fegin

1 IMB - Institut de Mathématiques de Bordeaux

A generalization of the classical random sampling scheme is suggested. Based on the proposed generalization one can derive many new minimum variance unbiased estimators for probabilities, as well as for other functions of unknown parameters, for the multivariate Polya, the multivariate negative Polya, the multinomial, the multivariate hypergeometric, the multivariate Poisson, and the Wishart probability distributions.

Mots clés: Generalized random sampling scheme; unbiased estimators; probabilities of linear inequalities; multivariate discrete distributions; multivariate Polya distribution; multivariate negative Polya distribution; multivariate Poisson distribution; Wishart distribution

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Applications [stat.AP]; Méthodologie [stat.ME]

Yan Lumelskii, Vassily Voinov, Mikhail Nikulin, Paul Paul Fegin. .On a generalization of the classical random sampling scheme and unbiased estimation, by Ya.Lumelskii, V.Voinov, M.Nikulin and P.Fegin. Communications in Statistics - Theory and Methods, 2007, 36 (4), pp.693-705. ⟨10.1080/03610920601033793⟩. ⟨hal-00208047⟩