Calculate Tukey's Biweight Robust Mean

This calculates a robust average that is unaffected by outliers.

TukeyBiweight(x, const = 9, na.rm = FALSE,
              conf.level = NA, ci.type = "bca", R=1000, ...)

Arguments

x: a numeric vector
const: a constant. const is preassigned a value of 9 according to the Cook reference below but other values are possible.
na.rm: logical, indicating whether NA values should be stripped before the computation proceeds. Defaults to FALSE.
conf.level: confidence level of the interval. If set to NA (which is the default) no confidence interval will be calculated.
ci.type: The type of confidence interval required. The value should be any subset of the values "basic", "stud", "perc", "bca" or simply "all" which will compute all four types of intervals.
R: The number of bootstrap replicates. Usually this will be a single positive integer. For importance resampling, some resamples may use one set of weights and others use a different set of weights. In this case R would be a vector of integers where each component gives the number of resamples from each of the rows of weights.
...: the dots are passed to the function boot, when confidence intervalls are calculated.

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.

Value

A numeric mean.

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.

Author

Mikko Korpela <mikko.korpela@aalto.fi>

Examples

TukeyBiweight(rnorm(100))
#> [1] -0.167