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Missing Observations in Multivariate Statistics. IV: A Note on Simple Linear Regression

A. A. Afifi and R. M. Elashoff
Journal of the American Statistical Association
Vol. 64, No. 325 (Mar., 1969), pp. 359-365
DOI: 10.2307/2283745
Stable URL: http://www.jstor.org/stable/2283745
Page Count: 7
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Missing Observations in Multivariate Statistics. IV: A Note on Simple Linear Regression
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Abstract

In this note we examine the bias and small sample efficiency of certain estimators for the parameters of a linear regression function when some observations are missing. The estimators studies in this paper were suggested by the large sample study reported in this issue of the Journal. We conclude that our asymptotically unbiased estimators of β and μy∣ x have negligible bias in sample sizes as small as n = 20, and that our asymptotically unbiased estimator of σ2 may have an 8% bias when n = 20. The small sample and asymptotic efficiencies of these estimators are nearly the same for n = 60; when n = 20 the difference between these two efficiencies depends on the correlation coefficient ρ and the pattern of missing observations.

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