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Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals

Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals,10.1214/aoms/1177692377,The Annals of Mathematical Statistics,Louis A

Estimating Regression Coefficients by Minimizing the Dispersion of the Residuals   (Citations: 161)
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An appealing approach to the problem of estimating the regression coefficients in a linear model is to find those values of the coefficients which make the residuals as small as possible. We give some measures of the dispersion of a set of numbers, and define our estimates as those values of the parameters which minimize the dispersion of the residuals. We consider dispersion measures which are certain linear combinations of the ordered residuals. We show that the estimates derived from them are asymptotically equivalent to estimates recently proposed by Jureckova. In the case of a single parameter, we show that our estimate is a "weighted median" of the pairwise slopes $(Y_j - Y_i)/(c^j - c^i)$.
Journal: The Annals of Mathematical Statistics , vol. 43, no. 1972, pp. 1449-1458, 1972
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    • ...We are interested in asymptotic properties of the rank regression estimate of β0 defined by Jaeckel 1...

    Kristi Kuljuset al. Asymptotic properties of a rank estimate in linear regression with sym...

    • ...The LAD step can be seen as a rank-based estimator via Wilcoxon scores, to minimize the residual dispersion function given in Jaeckel (1972)...

    Chenlei Leng. VARIABLE SELECTION AND COEFFICIENT ESTIMATION VIA REGULARIZED RANK REG...

    • ...Rank-based estimates of the regression coefficients of an univariate linear model have been proposed by Jaeckel (1972) and Jureckova (1971), which achieved some robustness against outliers, while allowing the user a choice of scores for efficiency consideration...

    Weihua Zhou. A multivariate Wilcoxon regression estimate

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