tauLocScale: Robust tau-estimate of location and scale
In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description Usage Arguments Details Value References Examples

This implements Yohai & Zamar's tau-estimate of location and scale. The tau-estimate is the result of a three stage estimation process. First, initial estimates of location and scale are made. In this implementation the initial location and scale estimates μ0 and σ0 are the Harrell-Davis estimates of the median and median absolute deviation. The second stage uses a weight function corresponding to a bounded ψ function, tuned with tuning constant c1 for robustness in order to provide a robust estimate of location, μ. The second stage uses a ρ function with tuning constant c2 tuned for high efficiency to estimate the dispersion of the data around μ. The final scale estimate is adjusted with a consistency factor to ensure nominal efficiency at the Gaussian distribution. The default tuning constants are taken from Maronna & Zamar (2002), which yield 80% efficiency at both the Gaussian and Cauchy distributions, and provides a good balance between robustness and efficiency. The underlying implementation is a fast C++ algorithm. See details for more information.

1	tauLocScale(x, c1 = 4.5, c2 = 3, mu = TRUE)

`x`	a vector
`c1`	a tuning parameter. defaults to 4.5.
`c2`	a second tuning parameter. defaults to 3.
`mu`	whether or not the robust mean should also be returned. defaults to TRUE.

Weights are then defined using the bisquare weight function as w = (1 - (u / c1)^2)^2 \times I(|u| <= c1), where u = (x_i - μ0)/ σ0. The tau-estimate of location is then defined as μ = (Σ (x_i \times w_i)) / Σ w_i and the scale estimate as σ = √{σ0^2 /n \times Σ ρ_c2((x_i - μ)/ σ0)} , where ρ_c2 is the bisquare ρ function with tuning constant c2.

a numeric vector or numeric value

Yohai, R.A. and Zamar, R.H. (1998) "High breakdown point estimates of regression by means of the minimization of efficient scale. Journal of the American Statistical Association, 86:403–413.

Maronna, R.A. and Zamar, R.H. (2002) Robust estimates of location and dispersion of high-dimensional datasets. Technometrics 44(4), 307-317.