Displaying 21 – 40 of 49

Showing per page

An efficient estimator for Gibbs random fields

Martin Janžura (2014)

Kybernetika

An efficient estimator for the expectation f P ̣ is constructed, where P is a Gibbs random field, and f is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer [6], and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.

Approximated maximum likelihood estimation of parameters of discrete stable family

Lenka Slámová, Lev B. Klebanov (2014)

Kybernetika

In this article we propose a method of parameters estimation for the class of discrete stable laws. Discrete stable distributions form a discrete analogy to classical stable distributions and share many interesting properties with them such as heavy tails and skewness. Similarly as stable laws discrete stable distributions are defined through characteristic function and do not posses a probability mass function in closed form. This inhibits the use of classical estimation methods such as maximum...

Approximative solutions of stochastic optimization problems

Petr Lachout (2010)

Kybernetika

The aim of this paper is to present some ideas how to relax the notion of the optimal solution of the stochastic optimization problem. In the deterministic case, ε -minimal solutions and level-minimal solutions are considered as desired relaxations. We call them approximative solutions and we introduce some possibilities how to combine them with randomness. Relations among random versions of approximative solutions and their consistency are presented in this paper. No measurability is assumed, therefore,...

Asymptotic analysis of minimum volume confidence regions for location-scale families

M. Alama-Bućko, A. Zaigraev (2006)

Applicationes Mathematicae

An asymptotic analysis, when the sample size n tends to infinity, of the optimal confidence region established in Czarnowska and Nagaev (2001) is considered. As a result, two confidence regions, both close to the optimal one when n is sufficiently large, are suggested with a mild assumption on the distribution of a location-scale family.

Asymptotic normality and efficiency of variance components estimators with high breakdown points

Christine H. Müller (2000)

Discussiones Mathematicae Probability and Statistics

For estimating the variance components of a one-way random effect model recently Uhlig (1995, 1997) and Lischer (1996) proposed non-iterative estimators with high breakdown points. These estimators base on the high breakdown point scale estimators of Rousseeuw and Croux (1992, 1993), which they called Q-estimators. In this paper the asymptotic normal distribution of the new variance components estimators is derived so that the asymptotic efficiency of these estimators can be compared with that of...

Asymptotic normality of randomly truncated stochastic algorithms

Jérôme Lelong (2013)

ESAIM: Probability and Statistics

We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins–Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function, which are fairly...

Asymptotic properties of autoregressive regime-switching models

Madalina Olteanu, Joseph Rynkiewicz (2012)

ESAIM: Probability and Statistics

The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures [X. Liu and Y. Shao, Ann. Stat. 31 (2003) 807–832] and hidden Markov chains [E. Gassiat, Ann. Inst. Henri Poincaré 38 (2002) 897–906]. First, we study the case of mixtures of autoregressive models (i.e. independent...

Asymptotic properties of autoregressive regime-switching models

Madalina Olteanu, Joseph Rynkiewicz (2012)

ESAIM: Probability and Statistics

The statistical properties of the likelihood ratio test statistic (LRTS) for autoregressive regime-switching models are addressed in this paper. This question is particularly important for estimating the number of regimes in the model. Our purpose is to extend the existing results for mixtures [X. Liu and Y. Shao, Ann. Stat. 31 (2003) 807–832] and hidden Markov chains [E. Gassiat, Ann. Inst. Henri Poincaré 38 (2002) 897–906]. First, we study the case of mixtures of autoregressive models (i.e. independent...

Asymptotic properties of the growth curve model with covariance components

Ivan Žežula (1997)

Applications of Mathematics

We consider a multivariate regression (growth curve) model of the form Y = X B Z + ε , E ε = 0 , var ( vec ε ) = W Σ , where W = i = 1 k θ i V i and θ i ’s are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters { B i j } estimating simultaneously the first and the second order parameters.

Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes

Jiří Dvořák, Michaela Prokešová (2016)

Applications of Mathematics

We consider a flexible class of space-time point process models—inhomogeneous shot-noise Cox point processes. They are suitable for modelling clustering phenomena, e.g. in epidemiology, seismology, etc. The particular structure of the model enables the use of projections to the spatial and temporal domain. They are used to formulate a step-wise estimation method to estimate different parts of the model separately. In the first step, the Poisson likelihood approach is used to estimate the inhomogeneity...

Currently displaying 21 – 40 of 49