METHODOLOGY OF EXTREME VALUES ANALYSIS AND ITS APPLICATION FOR PARAMETER ESTIMATION OF GENERALIZED LINEAR MODELS

S. B. Trukhan, P. I. Bidyuk

Abstract


The article deals with methodology of extreme values treatment for building and estimating unknown parameters of generalized linear
models. As a mathematical tool for carrying out the research the extreme value theory was used that creates one of the directions in
mathematical statistics, and is related to investigating the extreme deviations from the median values in probability distributions. Also, the
methods of approximation statistical data to generalized extreme value distribution, the methods of estimating unknown parameters and
selecting an optimal threshold for extreme value models are discussed. The models of treatment extreme values are constructed which are based on actual statistical data and approach is proposed for their future application for estimating predictive models. The model with generalized Pareto distribution turned out to be acceptable for further use, because it has minimum value of observation error and the best approximation of observed curve to theoretical density function. The comparison of evaluation unknown models’ parameters using method of maximum likelihood and Bayesian approach leads to next conclusion. The Bayesian methods are efficient way to solve the problem of selection the best model, based on the received alternatives set and prior parameters values. In future studies it will be reasonable to consider the application of extreme value analysis to predicted generalized linear models.

Keywords


extreme value theory, generalized linear models, extreme value threshold, maximum likelihood method, Bayesian approach.

References


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DOI: https://doi.org/10.15588/1607-3274-2016-1-3



Copyright (c) 2016 S. B. Trukhan, P. I. Bidyuk

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