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A geometric perspective on weighted least squares and its connections to robustness

Abstract Number:

2038

Submission Type:

Contributed Abstract

Contributed Abstract Type:

Paper

Participants:

Jordan Bryan (1), Didong Li (2)

Institutions:

(1) University of North Carolina at Chapel Hill, N/A, (2) N/A, N/A

Co-Author:

Didong Li
N/A

First Author:

Jordan Bryan
University of North Carolina at Chapel Hill

Presenting Author:

Jordan Bryan
University of North Carolina at Chapel Hill

Abstract Text:

When independent errors in a linear model have non-identity covariance, the ordinary least squares (OLS) estimate of the model coefficients is less efficient than the weighted least squares (WLS) estimate. However, the practical application of weighted least squares is challenging due to its reliance on the unknown error covariance matrix. Although feasible weighted least squares (FWLS) estimates, which use an approximation of this matrix, often surpass OLS estimates in performance, this is not always the case. In some situations, FWLS estimates can be less efficient than OLS estimates. We characterize a subclass of FWLS estimates, which are guaranteed to have lower variance than the OLS estimate. The subclass of feasible weights corresponding to these FWLS estimates is defined by a growth-restricted monotonicity condition relative to the true error variances. Using this result, we show directly that a FWLS estimate need not be consistent to outperform the OLS estimate, and we highlight connections between the growth-restricted monotonicity condition and the asymptotic variance of a robust regression estimate derived from the t-distribution.

Keywords:

Sponsors:

International Statistical Institute

Tracks:

Miscellaneous

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