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Robust estimation for linear regression with asymmetric errors
Author(s) -
Bianco Ana M.,
Ben Marta Garcia,
Yohai Víctor J.
Publication year - 2005
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 - 10.1002/cjs.5550330404
Subject(s) - mathematics , asymptotic distribution , estimator , monte carlo method , robust regression , robustness (evolution) , statistics , consistency (knowledge bases) , strong consistency , linear regression , regression , regression analysis , exponential distribution , discrete mathematics , biochemistry , chemistry , gene
The authors propose a new class of robust estimators for the parameters of a regression model in which the distribution of the error terms belongs to a class of exponential families including the log‐gamma distribution. These estimates, which are a natural extension of the MM‐estimates for ordinary regression, may combine simultaneously high asymptotic efficiency and a high breakdown point. The authors prove the consistency and derive the asymptotic normal distribution of these estimates. A Monte Carlo study allows them to assess the efficiency and robustness of these estimates for finite samples.