We consider some results by D. Bernoulli and L. Euler on the method of maximum likelihood in parametric estimation. The statistical analysis is made by considering a parametric family with a shift parameter.
Generalizations of the additive hazards model are considered. Estimates of the regression parameters and baseline function are proposed, when covariates are random. The asymptotic properties of estimators are considered.
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.
Confidence intervals and regions for the parameters of a distribution are constructed, following the method due to L. N. Bolshev. This construction method is illustrated with Poisson, exponential, Bernouilli, geometric, normal and other distributions depending on parameters.
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...
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.
Since 1956, a large number of papers have been devoted to Stein's technique of obtaining improved estimators of parameters, for several statistical models. We give a brief review of these papers, emphasizing those aspects which are interesting from the point of view of the theory of unbiased estimation.
Este artículo desarrolla y comenta diversas correcciones de continuidad a las aproximaciones normal y chi-cuadrado de algunas distribuciones discretas.
Chi-squared goodness-of-fit test for the family of logistic distributions id proposed. Different methods of estimation of the unknown parameters θ of the family are compared. The problem of homogeneity is considered.
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