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Remarques sur le maximum de vraisemblance.

Catherine HuberMikhail Nikulin — 1997

Qüestiió

Some paradoxes on the maximum likelihood principle are presented and commented. We consider the properties of the maximum likelihood estimators as a particular case of the M-estimators. We propose a unified theory which includes non-dominated models. Several examples are given.

Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test.

Mikhail S. NikulinVassiliy G. Voinov — 1993

Qüestiió

We consider the problem of estimation of the value of a real-valued function u(θ), θ = (θ, ..., θ), on the basis of a sample from non-truncated or truncated multivariate Modified Power Series Distributions. Using the general theory of estimation and the results of Patil (1965) and Patel (1978) we give the tables of MVUE's for functions of parameter θ of trinomial, multinomial, negative-multinomial and left-truncated modified power series distributions. We have applied the properties of MVUE's and...

On the problem of the means of weighted normal populations.

Mikhail S. NikulinVassiliy G. Voinov — 1995

Qüestiió

An analytical problem, which arises in the statistical problem of comparing the means of two normal distributions, the variances of which -as well as their ratio- are unknown, is well known in the mathematical statistics as the Behrens-Fisher problem. One generalization of the Behrens-Fisher problem and different aspect concerning the estimation of the common mean of several independent normal distributions with different variances are considered and one solution is proposed.

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