TukeyBiweight: Calculate Tukey's Biweight Robust Mean

Description

This calculates a robust average that is unaffected by outliers.

Usage

TukeyBiweight(x, const = 9)

Arguments

a numeric vector

const

a constant. const is preassigned a value of 9 according to the Cook reference below but other values are possible.

Value

A numeric mean.

Details

This is a one step computation that follows the Affy whitepaper below, see page 22. const determines the point at which outliers are given a weight of 0 and therefore do not contribute to the calculation of the mean. const = 9 sets values roughly +/-6 standard deviations to 0. const = 6 is also used in tree-ring chronology development. Cook and Kairiukstis (1990) have further details. An exact summation algorithm (Shewchuk 1997) is used. When some assumptions about the rounding of floating point numbers and conservative compiler optimizations hold, summation error is completely avoided. Whether the assumptions hold depends on the platform, i.e. compiler and CPU.

References

Statistical Algorithms Description Document, 2002, Affymetrix. Cook, E. R. and Kairiukstis, L. A. (1990) Methods of Dendrochronology: Applications in the Environmental Sciences. Springer. ISBN-13: 978-0792305866. Mosteller, F. and Tukey, J. W. (1977) Data Analysis and Regression: a second course in statistics. Addison-Wesley. ISBN-13: 978-0201048544. Shewchuk, J. R. (1997) Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates. Discrete and Computational Geometry, 18(3):305-363. Springer.

Examples

Run this code

TukeyBiweight(rnorm(100))

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