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On minimax sequential procedures for exponential families of stochastic processes

Ryszard Magiera (1998)

Applicationes Mathematicae

The problem of finding minimax sequential estimation procedures for stochastic processes is considered. It is assumed that in addition to the loss associated with the error of estimation a cost of observing the process is incurred. A class of minimax sequential procedures is derived explicitly for a one-parameter exponential family of stochastic processes. The minimax sequential procedures are presented in some special models, in particular, for estimating a parameter of exponential families of...

On multiple periodic autoregression

Jiří Anděl (1987)

Aplikace matematiky

The model of periodic autoregression is generalized to the multivariate case. The autoregressive matrices are periodic functions of time. The mean value of the process can be a non-vanishing periodic sequence of vectors. Estimators of parameters and tests of statistical hypotheses are based on the Bayes approach. Two main versions of the model are investigated, one with constant variance matrices and the other with periodic variance matrices of the innovation process.

On periodic autoregression with unknown mean

Jiří Anděl, Asunción Rubio, Antonio Insua (1985)

Aplikace matematiky

If the parameters of an autoregressive model are periodic functions we get a periodic autoregression. In the paper the case is investigated when the expectation can also be a periodic function. The innovations have either constant or periodically changing variances.

On the Bayes estimators of the parameters of inflated modified power series distributions

Małgorzata Murat, Dominik Szynal (2000)

Discussiones Mathematicae Probability and Statistics

In this paper, we study the class of inflated modified power series distributions (IMPSD) where inflation occurs at any of support points. This class includes among others the generalized Poisson,the generalized negative binomial and the lost games distributions. We derive the Bayes estimators of parameters for these distributions when a parameter of inflation is known. First, we take as the prior distribution the uniform, Beta and Gamma distribution. In the second part of this paper, the prior...

On the convergence of extreme distributions under power normalization

E. M. Nigm (2008)

Applicationes Mathematicae

This paper deals with the convergence in distribution of the maximum of n independent and identically distributed random variables under power normalization. We measure the difference between the actual and asymptotic distributions in terms of the double-log scale. The error committed when replacing the actual distribution of the maximum under power normalization by its asymptotic distribution is studied, assuming that the cumulative distribution function of the random variables is known. Finally,...

On the frequentist and Bayesian approaches to hypothesis testing.

Elías Moreno, F. Javier Girón (2006)

SORT

Hypothesis testing is a model selection problem for which the solution proposed by the two main statistical streams of thought, frequentists and Bayesians, substantially differ. One may think that this fact might be due to the prior chosen in the Bayesian analysis and that a convenient prior selection may reconcile both approaches. However, the Bayesian robustness viewpoint has shown that, in general, this is not so and hence a profound disagreement between both approaches exists. In this paper...

On the outstanding elements and record values in the exponential and gamma populations.

G. S. Lingappaiah (1981)

Trabajos de Estadística e Investigación Operativa

Outstanding elements and recorded values are discussed in this paper as related to exponential and gamma populations. First, the problem of prediction is considered when there are available, k sets of independent observations from a general-type exponential distribution. In such a case, prediction of the nk-th record value in the k-th set is made in terms of ni-th (i = 1, ..., k-1) record values from other (k-1) sets. For this purpose a predictive distribution is obtained. Secondly, the distribution...

Optimal sequential multiple hypothesis tests

Andrey Novikov (2009)

Kybernetika

This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is characterized.

Parametric inference for mixed models defined by stochastic differential equations

Sophie Donnet, Adeline Samson (2008)

ESAIM: Probability and Statistics

Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants. A tuned...

Periodic autoregression with exogenous variables and periodic variances

Jiří Anděl (1989)

Aplikace matematiky

The periodic autoregressive process with non-vanishing mean and with exogenous variables is investigated in the paper. It is assumed that the model has also periodic variances. The statistical analysis is based on the Bayes approach with a vague prior density. Estimators of the parameters and asymptotic tests of hypotheses are derived.

Posterior odds ratios for selected regression hypotheses.

Arnold Zellner, Aloysius Siow (1980)

Trabajos de Estadística e Investigación Operativa

Bayesian posterior odds ratios for frequently encountered hypotheses about parameters of the normal linear multiple regression model are derived and discussed. For the particular prior distributions utilized, it is found that the posterior odds ratios can be well approximated by functions that are monotonic in usual sampling theory F statistics. Some implications of these finding and the relation of our work to the pioneering work of Jeffreys and others are considered. Tabulations of odd ratios...

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