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On random processes as an implicit solution of equations

Petr Lachout (2017)

Kybernetika

Random processes with convenient properties are often employed to model observed data, particularly, coming from economy and finance. We will focus our interest in random processes given implicitly as a solution of a functional equation. For example, random processes AR, ARMA, ARCH, GARCH are belonging in this wide class. Their common feature can be expressed by requirement that stated random process together with incoming innovations must fulfill a functional equation. Functional dependence is...

On randomized stopping times.

Concepción Arenas Solá (1990)

Trabajos de Estadística

In this note we give a proof of the fact that the extremal elements of the set of randomized stopping times are exactly the stopping times.

On reliability analysis of consecutive k -out-of- n systems with arbitrarily dependent components

Ebrahim Salehi (2016)

Applications of Mathematics

In this paper, we consider the linear and circular consecutive k -out-of- n systems consisting of arbitrarily dependent components. Under the condition that at least n - r + 1 components ( r ≤ n ) of the system are working at time t , we study the reliability properties of the residual lifetime of such systems. Also, we present some stochastic ordering properties of residual lifetime of consecutive k -out-of- n systems. In the following, we investigate the inactivity time of the component with lifetime T r : n at the system...

On risk minimizing strategies for default-free bond portfolio immunization

Marek Kałuszka, Alina Kondratiuk-Janyska (2004)

Applicationes Mathematicae

This paper presents new strategies for bond portfolio immunization which combine the time-honored duration with the M-Absolute measure defined by Nawalkha and Chambers (1996). The innovation consists in considering an average shock in a fixed time period as a random variable with mean μ or, alternatively, with normal distribution with mean μ and variance σ². Additionally, an extension to arbitrage free models of polynomial shocks is provided. Moreover, the Fisher and Weil model, the M-Absolute strategy...

On robust GMM estimation with applications in economics and finance

Ansgar Steland (2000)

Discussiones Mathematicae Probability and Statistics

Generalized Methods of Moments (GMM) estimators are a popular tool in econometrics since introduced by Hansen (1982), because this approach provides feasible solutions for many problems present in economic data where least squares or maximum likelihood methods fail when naively applied. These problems may arise in errors-in-variable regression, estimation of labor demand curves, and asset pricing in finance, which are discussed here. In this paper we study a GMM estimator for the rank modelingapproach...

On selecting the best features in a noisy environment

Jan Flusser, Tomáš Suk (1998)

Kybernetika

This paper introduces a novel method for selecting a feature subset yielding an optimal trade-off between class separability and feature space dimensionality. We assume the following feature properties: (a) the features are ordered into a sequence, (b) robustness of the features decreases with an increasing order and (c) higher-order features supply more detailed information about the objects. We present a general algorithm how to find under those assumptions the optimal feature subset. Its performance...

On sequential and fixed designs for estimation with comparisons and applications.

Mekki Terbeche, Broderick O. Oluyede, Ahmed Barbour (2005)

SORT

A fully sequential approach to the estimation of the difference of two population means for distributions belonging to the exponential family of distributions is adopted and compared with the best fixed design. Results on the lower bound for the Bayes risk due to estimation and expected costs are presented and shown to be of first order efficiency. Applications involving the Poisson and exponential distributions with gamma priors as well as the Bernouilli distribution with beta priors are given....

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