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BukuRegression with Symmetric Alpha-Stable Distributions
Bibliografi
Author: Uyanto, Stanislaus Suryadi
Bahasa: (EN )    
Penerbit: Department of Mathematics and Statistics The University of Melbourne     Tempat Terbit: Parkville    Tahun Terbit: 2003    
Jenis: Theses - Dissertation
Fulltext: Stanislaus S Uyanto Disertasi.pdf (2.6MB; 3 download)
Abstract
Gaussian distributions, also referred to as the Normal distributions, are in many ways the cornerstone of modern statistical theory. They are by far the most important distribution in the whole field of probability and statistics, and as well as being used to describe or model the probability structure of many real-life continuous variables. However, Gaussian distributions do not allow for large fluctuations or data that deviate from the ideal Gaussian model and are thus often inadequate for modeling high variability or heavy tailed distributions. Stable distributions, on the other hand, are a rich class of distributions that allow skewness and heavy tails. Stable distributions are direct generalization of the Gaussian distributions and share many of their familiar properties such as the stability property and the central limit theorems, and in fact include the Gaussian and Cauchy distributions. The method of linear regression with Gaussian distribution is incomplete in that it fails to deal with variables possessing heavy tails. To fill an important part of this gap, I contribute a particular type of non-Gaussian model of linear regression, based on the symmetric a-stable distribution, which is a natural generalization of the Gaussian distribution. First, we present a model for the dependence between two random variables from given distributions. Then the model is used as a class of linear regression models for continuous infinitely divisible distributions. The thesis primarily considers the problem of univariate linear regression with zero intercept where both the dependent and independent variables have an a-stable distribution. My research will be focused mainly on the methods for the estimation of the parameter of the regression model of the symmetric a-stable distributions and the parameter a of the stable distribution. Three methods of the parameter estimate of the regression model and two methods of the parameter a estimate are proposed. The practical rather than theoretical aspects are emphasized. Thousands of realizations of the a-stable random variables in this thesis were simulated using the rstab program in S-PLUS.
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