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Journal Article

Weighted Median Regression Estimates

Friedrich-Wilhelm Scholz
The Annals of Statistics
Vol. 6, No. 3 (May, 1978), pp. 603-609
Stable URL: http://www.jstor.org/stable/2958563
Page Count: 7

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Topics: Estimators, Linear regression, Confidence interval, Statistical median, Statism, Mathematics
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Weighted Median Regression Estimates
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Abstract

In the simple linear regression problem {Yi = α + β xi + ei i = 1,⋯, n, ei i.i.d. ∼ F continuous, x1 ≤ ⋯ ≤ xn known, α, β unknown} we investigate the following type of estimator: To each sij = (Yj - Yi)/(xj - xi) with $x_i < x_j$ attach weight wij and as estimator for β consider the median of this weight distribution over the sij. A confidence interval for β is found by taking certain quantiles of this weight distribution. The asymptotic behavior of both is investigated and conditions for optimal weights are given.

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