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Information contained in design points of experiments with correlated observations

Andrej Pázman (2010)

Kybernetika

A random process (field) with given parametrized mean and covariance function is observed at a finite number of chosen design points. The information about its parameters is measured via the Fisher information matrix (for normally distributed observations) or using information functionals depending on that matrix. Conditions are stated, under which the contribution of one design point to this information is zero. Explicit expressions are obtained for the amount of information coming from a selected...

Information inequalities for the minimax risk of sequential estimators (with applications)

Lesław Gajek, B. Mizera-Florczak (1998)

Applicationes Mathematicae

Information inequalities for the minimax risk of sequential estimators are derived in the case where the loss is measured by the squared error of estimation plus a linear functional of the number of observations. The results are applied to construct minimax sequential estimators of: the failure rate in an exponential model with censored data, the expected proportion of uncensored observations in the proportional hazards model, the odds ratio in a binomial distribution and the expectation of exponential...

Information matrices for some elliptically symmetric distributions.

Saralees Nadarajah, Samuel Kotz (2005)

SORT

The Fisher information matrices are derived for three of the most popular elliptically symmetric distributions: the Pearson type II, Pearson type VII and the Kotz type distributions. We hope the results could be important to the many researchers working in this area.

Information Matrix for Beta Distributions

Aryal, Gokarna, Nadarajah, Saralees (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 33C90, 62E99.The Fisher information matrix for three generalized beta distributions are derived.

Information Measure for Vague Symbols

Milan Mareš (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The structures of the fuzzy information theory are focused on the concept of fuzzy entropy, where the individual information of symbols is considered only implicitely. This paper aims to fill this gap and to study the concepts of fuzzy information. Special attention is paid to the typical fuzzy set theoretical paradigma of monotonicity of operations.

Insensitivity region for variance components in general linear model

Hana Boháčová (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In linear regression models the estimator of variance components needs a suitable choice of a starting point for an iterative procedure for a determination of the estimate. The aim of this paper is to find a criterion for a decision whether a linear regression model enables to determine the estimate reasonably and whether it is possible to do so when using the given data.

Instrumental weighted variables under heteroscedasticity. Part I – Consistency

Jan Ámos Víšek (2017)

Kybernetika

The proof of consistency instrumental weighted variables, the robust version of the classical instrumental variables is given. It is proved that all solutions of the corresponding normal equations are contained, with high probability, in a ball, the radius of which can be selected - asymptotically - arbitrarily small. Then also n -consistency is proved. An extended numerical study (the Part II of the paper) offers a picture of behavior of the estimator for finite samples under various types and levels...

Instrumental weighted variables under heteroscedasticity. Part II – Numerical study

Jan Ámos Víšek (2017)

Kybernetika

Results of a numerical study of the behavior of the instrumental weighted variables estimator – in a competition with two other estimators – are presented. The study was performed under various frameworks (homoscedsticity/heteroscedasticity, several level and types of contamination of data, fulfilled/broken orthogonality condition). At the beginning the optimal values of eligible parameters of estimatros in question were empirically established. It was done under the various sizes of data sets and...

Integrated Pearson family and orthogonality of the Rodrigues polynomials: A review including new results and an alternative classification of the Pearson system

G. Afendras, N. Papadatos (2015)

Applicationes Mathematicae

An alternative classification of the Pearson family of probability densities is related to the orthogonality of the corresponding Rodrigues polynomials. This leads to a subset of the ordinary Pearson system, the so-called Integrated Pearson Family. Basic properties of this family are discussed and reviewed, and some new results are presented. A detailed comparison between the Integrated Pearson Family and the ordinary Pearson system is presented, including an algorithm that enables one to decide...

Intelligent financial time series forecasting: A complex neuro-fuzzy approach with multi-swarm intelligence

Chunshien Li, Tai-Wei Chiang (2012)

International Journal of Applied Mathematics and Computer Science

Financial investors often face an urgent need to predict the future. Accurate forecasting may allow investors to be aware of changes in financial markets in the future, so that they can reduce the risk of investment. In this paper, we present an intelligent computing paradigm, called the Complex Neuro-Fuzzy System (CNFS), applied to the problem of financial time series forecasting. The CNFS is an adaptive system, which is designed using Complex Fuzzy Sets (CFSs) whose membership functions are complex-valued...

Intermittent estimation for finite alphabet finitarily Markovian processes with exponential tails

Gusztáv Morvai, Benjamin Weiss (2021)

Kybernetika

We give some estimation schemes for the conditional distribution and conditional expectation of the the next output following the observation of the first n outputs of a stationary process where the random variables may take finitely many possible values. Our schemes are universal in the class of finitarily Markovian processes that have an exponential rate for the tail of the look back time distribution. In addition explicit rates are given. A necessary restriction is that the scheme proposes an...

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