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Estimates of regression coefficients based on the sign covariance matrix
Author(s) -
Ollila Esa,
Oja Hannu,
Hettmansperger Thomas P.
Publication year - 2002
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00344
Subject(s) - mathematics , multivariate normal distribution , asymptotic distribution , statistics , covariance matrix , matrix t distribution , estimator , multivariate statistics , regression analysis , covariance
Summary. A new estimator of the regression parameters is introduced in a multivariate multiple‐regression model in which both the vector of explanatory variables and the vector of response variables are assumed to be random. The affine equivariant estimate matrix is constructed using the sign covariance matrix (SCM) where the sign concept is based on Oja's criterion function. The influence function and asymptotic theory are developed to consider robustness and limiting efficiencies of the SCM regression estimate. The estimate is shown to be consistent with a limiting multinormal distribution. The influence function, as a function of the length of the contamination vector, is shown to be linear in elliptic cases; for the least squares (LS) estimate it is quadratic. The asymptotic relative efficiencies with respect to the LS estimate are given in the multivariate normal as well as the t ‐distribution cases. The SCM regression estimate is highly efficient in the multivariate normal case and, for heavy‐tailed distributions, it performs better than the LS estimate. Simulations are used to consider finite sample efficiencies with similar results. The theory is illustrated with an example.