Robust regression by iteratively reweighted least squares

Least squares gives a single bad row unbounded influence. The biweight bounds it and, past the tuning constant, removes it. The scale is re-estimated by MAD on every sweep, so the weights are not decided by a scale the outliers themselves inflated.

Usage

Tukrr(X, y, c = 4.685, n_iter = 25)

Arguments

X

Design matrix; supply your own intercept column.

y

Response.

c

Tuning constant.

n_iter

Reweighting sweeps.

Value

List with estimate, scale, weights, fitted, resid, n.

Details

Determinism: fixed sweeps, ordinary least squares start, no tolerance.

Formula: iterate \(beta = argmin sum w_i (y_i - x_i primebeta)^2\) with \(w_i = [1 - (r_i/(c s))^2]^2\) inside and 0 outside.

References

Beaton, A. E. & Tukey, J. W. (1974). Technometrics 16:147-185; Holland, P. W. & Welsch, R. E. (1977). Commun Statist 6:813-827.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Tukrr(V, V)
#> $estimate
#> [1] 1
#> 
#> $scale
#> [1] 1
#> 
#> $weights
#> [1] 1 1 1 1 1 1 1 1
#> 
#> $fitted
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $resid
#> [1] 0 0 0 0 0 0 0 0
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Biweight IRLS robust regression"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"