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A LINEAR MODEL WITH ERRORS LACKING A VARIANCE II 1
Author(s) -
Chambers R. L.,
Heathcote C. R.
Publication year - 1978
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1978.tb01302.x
Subject(s) - estimator , mathematics , moment (physics) , statistics , least squares function approximation , least absolute deviations , variance (accounting) , absolute deviation , generalized least squares , standard deviation , physics , accounting , classical mechanics , business
Summary Numerical results are presented for estimates of the parameters in the linear model Y =βX +ε in which X is normally distributed and ε is symmetric stable. The study complements an earlier paper of the same title and the main concern is with numerical comparisons between four estimates of β; the least squares estimate, the minimum absolute deviations estimate, and two moment estimates of the form derived in Chambers and Heathcote (1975). The generation of fifty independent sets of observations (X j , Y j ), j = 1,2, …, n for each of n = 100, 500 and selected combinations of parameter values provided the basis of the results. It is indicated that the moment estimators and the minimum absolute deviation estimator performed comparably, and are a significant improvement on the least squares estimator. The main conclusion is that one of the moment estimates, based on a two stage adaptive procedure and denoted by β¯ n (t a ) below, is generally the most useful of the four.