Robust Line Estimation With Errors in Both Variables / Michael L. Brown.

By:

Brown, Michael L

Contributor(s):

National Bureau of Economic Research

Material type: Text

TextSeries: Working Paper Series (National Bureau of Economic Research) ; no. w0083.Publication details: Cambridge, Mass. National Bureau of Economic Research 1975.Description: 1 online resource: illustrations (black and white)Online resources:

Available additional physical forms:

Hardcopy version available to institutional subscribers

Abstract: The estimator holding the central place in the theory of the multivariate "errors-in-the-variables" (EV) model results from performing orthogonal recession on variables rescaled according to the covariance matrix of the errors [7]. Our first principal finding, via Monte Carlo on the univariate model, essentially relegates this estimator to use only in large samples on very well-behaved data, i.e., with no trace of outlier contamination. A modification, requiring a robust preliminary slope, is proposed that essentially sets out the generalization to EV of the w-estimator in regression. It is demonstrated that the modification is robust to outlier contamination even in small samples, given a sufficiently good preliminary estimator. A candidate for a preliminary slope estimator based on the data is proposed arid its performance under simulation examined. Least-absolute residuals estimation in EV is cited as an alternative candidate.

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Previous	nber w0080 Inequality: Earnings vs. Human Wealth /	nber w0081 The Parental Bequest to Children /	nber w0082 Certain Aspects of Generalized Box-Jenkins Models /	nber w0083 Robust Line Estimation With Errors in Both Variables /	nber w0084 A Comparison of Two Simple Methods for Obtaining Robust Confidence Intervals /	nber w0085 On the Identification of Time Varying Structures /	nber w0086 THe Use of the Box Step Method in Discrete Optimization /	Next

May 1975.

The estimator holding the central place in the theory of the multivariate "errors-in-the-variables" (EV) model results from performing orthogonal recession on variables rescaled according to the covariance matrix of the errors [7]. Our first principal finding, via Monte Carlo on the univariate model, essentially relegates this estimator to use only in large samples on very well-behaved data, i.e., with no trace of outlier contamination. A modification, requiring a robust preliminary slope, is proposed that essentially sets out the generalization to EV of the w-estimator in regression. It is demonstrated that the modification is robust to outlier contamination even in small samples, given a sufficiently good preliminary estimator. A candidate for a preliminary slope estimator based on the data is proposed arid its performance under simulation examined. Least-absolute residuals estimation in EV is cited as an alternative candidate.