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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 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 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 some Mixture Distributions

Nakhi, Y. Ben, Kalla, S.L. (2004)

Fractional Calculus and Applied Analysis

The aim of this paper is to establish some mixture distributions that arise in stochastic processes. Some basic functions associated with the probability mass function of the mixture distributions, such as k-th moments, characteristic function and factorial moments are computed. Further we obtain a three-term recurrence relation for each established mixture distribution.

On the asymptotic variance in the central limit theorem for particle filters

Benjamin Favetto (2012)

ESAIM: Probability and Statistics

Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends...

On the asymptotic variance in the central limit theorem for particle filters

Benjamin Favetto (2012)

ESAIM: Probability and Statistics

Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends...

On the autocorrelation function of a trended series.

Cecilio Mar Molinero (1985)

Qüestiió

Equations are derived for the autocorrelation function of a trended series. The special case of a linear trend is analysed in detail. It is shown that the zero of the autocorrelation function of a trended series is, in general, only dependent on the length of the series. This result is valid for stochastic and deterministic trends.

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