lawstat (version 3.3)

symmetry.test: Test of Symmetry

Description

Perform test for symmetry about an unknown median. Users can choose among the Cabilio--Masaro test Cabilio_Masaro_1996lawstat, the Mira test Mira_1999lawstat, or the MGG test Miao_etal_2006lawstat; and between using asymptotic distribution of the respective statistics or a distribution from \(m\)-out-of-\(n\) bootstrap Lyubchich_etal_2016_symmetrylawstat. Additionally to the general distribution asymmetry, the function allows to test for negative or positive skeweness (see the argument side). NAs from the data are omitted.

Usage

symmetry.test(x, option = c("MGG", "CM", "M"), side = c("both", "left",
  "right"), boot = TRUE, B = 1000, q = 8/9)

Arguments

x

data to be tested for symmetry.

option

test statistic to be applied. The options include statistic by Miao_etal_2006;textuallawstat (default), Cabilio_Masaro_1996;textuallawstat, and Mira_1999;textuallawstat.

side

choice from the three possible alternative hypotheses: general distribution asymmetry (side = "both", default), left skewness (side = "left"), or right skewness (side = "right").

boot

logical value indicates whether \(m\)-out-of-\(n\) bootstrap will be used to obtain critical values (default), or asymptotic distribution of the chosen statistic.

B

number of bootstrap replications to perform (default is 1000).

q

scalar from 0 to 1 to define a set of possible \(m\) for the \(m\)-out-of-\(n\) bootstrap. Default q = 8/9. Possible \(m\) are then set as the values unique(round(n*(q^j)) greater than 4, where n = length(x) and j = c(0:20).

Value

A list of class "htest" with the following components:

method

name of the method.

data.name

name of the data.

statistic

value of the test statistic.

p.value

\(p\)-value of the test.

alternative

alternative hypothesis.

estimate

bootstrap optimal \(m\) (given in the output only if bootstrap was used, i.e., boot = TRUE).

Details

If the bootstrap option is used (boot = TRUE), a bootstrap distribution is obtained for each candidate subsample size \(m\). Then, a heuristic method Bickel_etal_1997,Bickel_Sakov_2008lawstat is used for the choice of optimal \(m\). Specifically, we use the Wasserstein metric Ruschendorf_2001lawstat to calculate distances between different bootstrap distributions and select \(m\), which corresponds to the minimal distance. See Lyubchich_etal_2016_symmetry;textuallawstat for more details.

References

Examples

# NOT RUN {
data(zuni) #run ?zuni to see the data description
symmetry.test(zuni[,"Revenue"], boot = FALSE)

# }