Robust Regression Analysis for Non-Normal Situations under Symmetric Distributions Arising In Medical Research

Ganguly, Shyam S.

doi:10.22237/jmasm/1398918480

Cited by 4 publications

(1 citation statement)

References 22 publications

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“…It is obvious that the key to the use of MLE is the a priori determination of the type of probability distribution. Note that in addition to the EPD family, many different types of symmetric distributions are used to solve the problems of regression analysis: elliptical laws (logistic, Cauchy, Student t-distribution) [36][37][38], various Gaussian distributions [39,40]. In addition, there are specially developed models of symmetric distributions that make it possible to change the value of the excess coefficient and the severity of the tails of regression errors [41,42].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Estimating parameters of linear regression with an exponential power distribution of errors by using a polynomial maximization method

Zabolotnii

Khotunov

Chepynoha

et al. 2021

EEJET

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This paper considers the application of a method for maximizing polynomials in order to find estimates of the parameters of a multifactorial linear regression provided the random errors of the regression model follow an exponential power distribution. The method used is conceptually close to a maximum likelihood method because it is based on the maximization of selective statistics in the neighborhood of the true values of the evaluated parameters. However, in contrast to the classical parametric approach, it employs a partial probabilistic description in the form of a limited number of statistics of higher orders. The adaptive algorithm of statistical estimation has been synthesized, which takes into consideration the properties of regression residues and makes it possible to find refined values for the estimates of the parameters of a linear multifactorial regression using the numerical Newton-Rafson iterative procedure. Based on the apparatus of the quantity of extracted information, the analytical expressions have been derived that make it possible to analyze the theoretical accuracy (asymptotic variances) of estimates for the method of maximizing polynomials depending on the magnitude of the exponential power distribution parameters. Statistical modeling was employed to perform a comparative analysis of the variance of estimates obtained using the method of maximizing polynomials with the accuracy of classical methods: the least squares and maximum likelihood. Regions of the greatest efficiency for each studied method have been constructed, depending on the magnitude of the parameter of the form of exponential power distribution and sample size. It has been shown that estimates from the polynomial maximization method may demonstrate a much lower variance compared to the estimates from a least-square method. And, in some cases (for flat-topped distributions and in the absence of a priori information), may exceed the estimates from the maximum likelihood method in terms of accuracy

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