parody (version 1.30.0)

calout.detect: interface to modular calibrated outlier detection system

Description

Various classical and resistant outlier detection procedures are provided in which the outlier misclassification rate for Gaussian samples is fixed over a range of sample sizes.

Usage

calout.detect(x, alpha = 0.05, method = c("GESD", "boxplot", "medmad",  "shorth", "hybrid"), k = ((length(x)%%2) * floor(length(x)/2) +  (1 - (length(x)%%2)) * (length(x)/2 - 1)), scaling, ftype,  location, scale, gen.region = function(x, location, scale,  scaling, alpha) { g <- scaling(length(x), alpha) location(x) + c(-1, 1) * g * scale(x) })

Arguments

x

data vector, NAs not allowed

alpha

outlier mislabeling rate for Gaussian samples

method

one of c("GESD", "boxplot", "medmad", "shorth"); the first selects generalized extreme studentized deviate (Rosner, 1983); the second selects calibrated boxplot rules; the third selects the method of Hampel in which the sample median is used for location estimation, and the median absolute deviation is used for scale; and the fourth selects Rousseeuw's rule, with the midpoint of the shortest half sample used as location estimator, and the length of this shortest half sample used as scale estimator.

An important characteristic of the GESD procedure is that the critical values for outlier labeling are calibrated to preserve the overall Type I error rate of the procedure given that there will be k tests, whether or not any outliers are present in the data.

k

for GESD, the prespecified upper limit on the number of outliers suspected in the data; defaults to ``half'' the sample size.

scaling

for resistant methods, scaling is a sample-size dependent function that tells how many multiples of the scale estimate should be laid off on each side of the location estimate to demarcate the inlier region; see Davies and Gather (1993) for the general formulation. The main contribution of this program consists in the development of scaling functions that ``calibrate'' outlier detection in Gaussian samples. The scaling function is assumed to take two arguments, n and alpha, and it should return a real number.

If method=="boxplot", the default value scaling=box.scale will confine the probability of erroneous detection of one or more outliers in a pure Gaussian sample to alpha. The use of scaling=function(n,alpha) 1.5 gives the standard boxplot outlier labeling rule.

If method=="medmad", the use of scaling=hamp.scale.4 will confine the outlier mislabeling rate to alpha; whereas the use of scaling=function(n,alpha) 5.2 gives Hampel's rule (Davies and Gather, 1993, p. 790).

If method=="shorth", the default value scaling=shorth.scale will confine the outlier mislabeling rate to alpha.

ftype

The type of ``fourth'' calculation; the standard definition of the fourth uses 0.5 * floor((n + 3)/2) to obtain the sortile of the fourth value; Hoaglin and Iglewicz (1987) give an ``ideal'' definition of the fourth which reduces the dependence of boxplot-based outlier detection performance (in small samples) on the quantity n mod 4.

location

a function on a vector returning a location estimate

scale

a function on a vector returning a scale estimate

gen.region

a function of x, location, scale, scaling, alpha that returns the inlier region as a 2-vector

Value

a list with components ind (indices of outliers in the input vector) val (values of these components) and outlier.region, which is only defined for the resistant methods.

References

Davies and Gather (1993 JASA), Rousseeuw and Leroy (1988 Stat Neer), Rosner (1983 Technom), Hoaglin and Iglewicz (1987 JASA), Carey, Walters, Wager and Rosner (1997 Technom)

Examples

lead <- c(83, 70, 62, 55, 56, 57, 57, 58, 59, 50, 51, 52, 52, 52, 54, 54, 45, 46, 48, 
        48, 49, 40, 40, 41, 42, 42, 44, 44, 35, 37, 38, 38, 34, 13, 14)

calout.detect(lead,alpha=.05,method="boxplot",ftype="ideal")
calout.detect(lead,alpha=.05,method="GESD",k=5)
calout.detect(lead,alpha=.05,method="medmad",scaling=hamp.scale.3)
calout.detect(lead,alpha=.05,method="shorth")