The paper concerns with a heteroscedastic random coefficient autoregressive model (RCA) of the form $X_t=b_t{X}_{t-1}+Y_t$. Two different procedures for estimating ${\sigma }_t^2=E{Y}_t^2,{\sigma }_b^2=E{b}_t^2$ or ${\sigma }_B^2=E{(b_t-E{b}_t)}^2$, respectively, are described under the special seasonal behaviour of ${\sigma }_t^2$. For both types of estimators strong consistency and asymptotic normality are proved.

A complete and sufficient statistic is found for stationary marked Poisson processes with a parametric distribution of marks. Then this statistic is used to derive the uniformly best unbiased estimator for the length density of a Poisson or Cox segment process with a parametric primary grain distribution. It is the number of segments with reference point within the sampling window divided by the window volume and multiplied by the uniformly best unbiased estimator of the mean segment length.

We introduce and study the behavior of estimators of changes in the mean value of a sequence of independent random variables in the case of so called epidemic alternatives which is one of the variants of the change point problem. The consistency and the limit distribution of the estimators developed for this situation are shown. Moreover, the classical estimators used for `at most change' are examined for the studied situation.

A number of papers has been published on the estimation problem in location models with abrupt changes (e.g., Cs" orgő and Horváth (1996)). In the present paper we focus on estimators in location models with gradual changes. Estimators of the parameters are proposed and studied. It appears that the limit behavior (both the rate of consistency and limit distribution) of the estimators of the change point in location models with abrupt changes and gradual changes differ substantially.

We investigate estimators of the asymptotic variance ${\sigma }^2$ of a $d$–dimensional stationary point process $\Psi$ which can be observed in convex and compact sampling window $W_n=nW$. Asymptotic variance of $\Psi$ is defined by the asymptotic relation $Var\left(\Psi \left(W_n\right)\right)\sim {\sigma }^2\left|W_n\right|$ (as $n\to \infty$) and its existence is guaranteed whenever the corresponding reduced covariance measure ${\gamma }_{\mathrm{red}}^{\left(2\right)}(·)$ has finite total variation. The three estimators discussed in the paper are the kernel estimator, the estimator based on the second order intesity of the point process and the...

A partir de una muestra de datos de supervivencia que contiene valores no observados en las covariantes de interés, presentamos una metodología que permite extraer toda la información contenida en covariantes completamente observadas, que estén fuertemente correlacionadas con las citadas covariantes de interés. El enfoque utilizado es completamente paramétrico y se basa en el método de máxima verosimilitud. Mostramos las dificultades, tanto de índole práctica como filosófica, que aparecen en la...

Evolutionary computation is a discipline that has been emerging for at least 40 or 50 years. All methods within this discipline are characterized by maintaining a set of possible solutions (individuals) to make them successively evolve to fitter solutions generation after generation. Examples of evolutionary computation paradigms are the broadly known Genetic Algorithms (GAs) and Estimation of Distribution Algorithms (EDAs). This paper contributes to the further development of this discipline by...

In this paper we focus on the problem of using a genetic algorithm for model selection within a Bayesian framework. We propose to reduce the model selection problem to a search problem solved using evolutionary computation to explore a posterior distribution over the model space. As a case study, we introduce ELeaRNT (Evolutionary Learning of Rich Neural Network Topologies), a genetic algorithm which evolves a particular class of models, namely, Rich Neural Networks (RNN), in order to find an optimal...

In this paper it is shown how one can work out exact distributions of estimators and test statistics in the model of a regression line for the threshold parameter with exponential distribution of errors. This is done on a test statistics which is related to a problem of Zvára [Zvara95].

The failure time distribution for various items often follows a shifted (two-parameter) exponential model and not the traditional (one-parameter) exponential model. The shifted exponential is very useful in practice, in particular in the engineering, biomedical sciences and industrial quality control when modeling time to event or survival data. The open problem of simultaneous testing for differences in origin and scale parameters of two shifted exponential distributions is addressed. Two exact...