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robust regression


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A method of regression that is not greatly affected by discordant observations. The most usual method for obtaining regression estimates is ordinary least squares (OLS), which is quite sensitive to the presence of outliers. One example of a robust alternative to OLS is iteratively reweighted least squares.

When there is a single x-variable a simple alternative robust method is as follows.1. Divide the data into three approximately equal-sized groups according to the sizes of the x-values. Call the groups L (low), M (medium), and H (High). Find the medians of the x-values and y-values in each group: (xL, yL), (xM, yM), and (xH, yH).2. Estimate the slope of the line as β̃ = yHyLxHxL.3. Estimate the intercept as 13{(yHβ̃xH) + (yMβ̃xM) + (yLβ̃xL)}.The resulting line is known as the median-median line or the resistant line.

1. Divide the data into three approximately equal-sized groups according to the sizes of the x-values. Call the groups L (low), M (medium), and H (High). Find the medians of the x-values and y-values in each group: (xL, yL), (xM, yM), and (xH, yH).

2. Estimate the slope of the line as β̃ = yHyLxHxL.

3. Estimate the intercept as 13{(yHβ̃xH) + (yMβ̃xM) + (yLβ̃xL)}.

Subjects: Probability and Statistics.


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