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Estimation of regression equation with cauchy disturbances
Author(s) -
Kadiyala K.R.,
Murthy K.S.R.
Publication year - 1977
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315088
Subject(s) - mathematics , cauchy distribution , estimator , statistics , maximum likelihood sequence estimation , monte carlo method , regression analysis , estimating equations , linear regression , regression
In this paper we present two methods of estimating a linear regression equation with Cauchy disturbances. The first method uses the maximum likelihood principle and therefore the estimators obtained are consistent. The asymptotic covariance is derived which provides with the necessary statistics for the purpose of making inference in large samples. The second method is the method of least lines which minimizes the sum of absolute errors ( MSAE ) from the fitted regression. Then these two methods are compared through a Monte Carlo study. The maximum likelihood method emerges superior over the MSAE method. However, the MSAE procedure which does not depend on the distribution of the error term appears to be a close competitor to the maximum likelihood estimator.