tw: Tracy-Widom test

Description Usage Arguments Value Author(s) References Examples

View source: R/TW_main.R

Description

Find the significant eigenvalues of a matrix.

Usage

1
tw(eigenvalues, eigenL, criticalpoint = 2.0234)

Arguments

eigenvalues

a numeric vector whose elements are the eigenvalues of a matrix. The values should be sorted in the descending order.

eigenL

the number of eigenvalues.

criticalpoint

a numeric value corresponding to the significance level. If the significance level is 0.05, 0.01, 0.005, or 0.001, the criticalpoint should be set to be 0.9793, 2.0234, 2.4224, or 3.2724, accordingly. The default is 2.0234.

Value

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

statistic
a vector of the Tracy-Widom statistics.
alternative
a character string describing the alternative hypothesis.
method
a character string indicating the type of test performed.
data.name
a character string giving the name of the data.
SigntEigenL
the number of significant eigenvalues.

Author(s)

Lin Wang, Wei Zhang, and Qizhai Li.

References

N Patterson, AL Price, and D Reich. Population Structure and Eigenanalysis. PloS Genetics. 2006; 2(12): 2074-2093.

CA Tracy and H Widom. Level-Spacing Distributions and the Airy Kernel. Communications in Mathematical Physics. 1994; 159(1): 151-174.

A Bejan. Tracy-Widom and Painleve II: Computational Aspects and Realisation in S-Plus. In First Workshop of the ERCIM Working Group on Computing and Statistics. 2008, Neuchatel, Switzerland.

www.vitrum.md/andrew/MScWrwck/codes.txt

Examples

1
tw(eigenvalues = c(5, 3, 1, 0), eigenL = 4, criticalpoint = 2.0234)

Example output

Loading required package: cluster
Loading required package: mvtnorm
Loading required package: combinat

Attaching package: 'combinat'

The following object is masked from 'package:utils':

    combn

Loading required package: fExtremes
Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fBasics


Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
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Loading required package: fGarch
Loading required package: fTrading

	Tracy-Wisdom test

data:  c(5, 3, 1, 0)
TW1 = -0.82427, TW2 = -0.60186, TW3 = -0.55525, TW4 = NaN
alternative hypothesis: the eigenvalue is significant

AssocTests documentation built on Nov. 17, 2017, 4:28 a.m.

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