### A. A. Markov, ses probabilités en chaîne et les statistiques linguistiques

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This paper presents a Bayesian significance test for a change in mean when observations are not independent. Using a noninformative prior, a unconditional test based on the highest posterior density credible set is determined. From a Gibbs sampler simulation study the effect of correlation on the performance of the Bayesian significance test derived under the assumption of no correlation is examined. This paper is a generalization of earlier studies by KIM (1991) to not independent observations.

We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi [Stoch. Proc. Appl. 84 (1999) 313–342]. The proof uses a new variant of the Lindeberg method: the behavior of the partial sums is compared to that of partial sums of dependent Gaussian random variables. We also discuss a few applications in statistics which show that our central limit theorem is tailor-made for statistics...

In this paper some of the cointegration tests applied to a single equation are compared. Many of the existent cointegration tests are simply extensions of the unit root tests applied to the residuals of the cointegrating regression and the habitual ${H}_{0}$ is no cointegration. However, some non residual-based tests and some tests of the opposite null hypothesis have recently appeared in literature. Monte Carlo simulations have been used for the power comparison of the nine selected tests ($ADF$, ${\widehat{Z}}_{\alpha}$, ${\widehat{Z}}_{t}$, $DHS$,...

In this paper a problem of consumption and investment is presented as a model of a discounted Markov decision process with discrete-time. In this problem, it is assumed that the wealth is affected by a production function. This assumption gives the investor a chance to increase his wealth before the investment. For the solution of the problem there is established a suitable version of the Euler Equation (EE) which characterizes its optimal policy completely, that is, there are provided conditions...

A system composed from a set of independent and identical parallel units is considered and its resistance (survival) against an increasing load is modelled by a counting process model, in the framework of statistical survival analysis. The objective is to estimate the (nonparametrized) hazard function of the distribution of loads breaking the units of the system (i. e. their breaking strengths), to derive the large sample properties of the estimator, and to propose a goodness-of-fit test. We also...

The problem of estimating the intensity of a non-stationary Poisson point process arises in many applications. Besides non parametric solutions, e. g. kernel estimators, parametric methods based on maximum likelihood estimation are of interest. In the present paper we have developed an approach in which the parametric function is represented by two-dimensional beta-splines.