asbio (version 1.3-1)

huber.NR: Huber M-estimator iterative least squares algorithm

Description

Algorithm for calculating fully iterated or one step Huber M-estimators of location.

Usage

huber.NR(x, c = 1.28, iter = 20)

Arguments

x

A vector of quantitative data

c

Bend criterion. The value c = 1.28 gives 95 percent efficiency of the mean given normality.

iter

Maximum number of iterations

Value

Returns iterative least squares iterations which converge to Huber's M-estimator. The first element in the vector is the sample median. The second element is the Huber one-step estimate.

Details

The Huber M-estimator is a robust high efficiency estimator of location that has probably been under-utilized by biologists. It is based on maximizing the likelihood of a weighting function. This is accomplished using an iterative least squares process. The Newton Raphson algorithm is used here. The function usually converges fairly quickly < 10 iterations. The function uses the Median Absolute Deviation function, mad. Note that if MAD = 0, then NA is returned.

References

Huber, P. J. (2004) Robust Statistics. Wiley.

Wilcox, R. R. (2005) Introduction to Robust Estimation and Hypothesis Testing, Second Edition. Elsevier, Burlington, MA.

See Also

huber.one.step, huber.mu, mad

Examples

x<-rnorm(100)
huber.NR(x)