tw {AssocTests}

Tracy-Widom test

Description

Find the significant eigenvalues of a matrix.

Usage

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

Lin Wang, Wei Zhang, and Qizhai Li. AssocTests: An R Package for Genetic Association Studies. Journal of Statistical Software. 2020; 94(5): 1-26.

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.

A Bejan. Largest eigenvalues and sample covariance matrices. MSc Dissertation, the university of Warwick. 2005. (This function was written by A Bejan and publicly downloadable.)

Examples

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