WilksW

WilksW[m1,m2]

gives Wilks's for the matrices m1 and m2.

Details

  • WilksW[m1,m2] gives Wilks's between m1 and m2.
  • Wilks's is a measure of linear dependence based on partitions of the pooled covariance matrix.
  • Wilks's is computed as 1-TemplateBox[{Sigma}, Det]/(TemplateBox[{{Sigma, _, {(, 11, )}}}, Det] TemplateBox[{{Sigma, _, {(, 22, )}}}, Det]) where is the covariance matrix of the pooled sample which can be partitioned into , where and correspond to the covariance matrices of the individual datasets.
  • The arguments m1 and m2 can be any realvalued matrices or vectors of equal length.

Examples

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Basic Examples  (3)

Compute Wilks's for two matrices:

Wilks's for two vectors:

Wilks's for a matrix and a vector:

Scope  (3)

Wilks's is typically used to detect linear dependence between random matrices:

Values tend to be large for dependent matrices:

The value is much smaller for independent matrices:

Wilks's for machine-precision reals:

Use arbitrary precision:

Properties & Relations  (3)

Wilks's measures linear dependence:

Wilks's cannot detect nonlinear dependency:

HoeffdingD can be used to detect some nonlinear dependence structures:

The statistical significance of can be tested using WilksWTest:

Alternatively, use IndependenceTest to automatically choose a test:

Wolfram Research (2012), WilksW, Wolfram Language function, https://reference.wolfram.com/language/ref/WilksW.html.

Text

Wolfram Research (2012), WilksW, Wolfram Language function, https://reference.wolfram.com/language/ref/WilksW.html.

BibTeX

@misc{reference.wolfram_2021_wilksw, author="Wolfram Research", title="{WilksW}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/WilksW.html}", note=[Accessed: 27-November-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_wilksw, organization={Wolfram Research}, title={WilksW}, year={2012}, url={https://reference.wolfram.com/language/ref/WilksW.html}, note=[Accessed: 27-November-2021 ]}

CMS

Wolfram Language. 2012. "WilksW." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WilksW.html.

APA

Wolfram Language. (2012). WilksW. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WilksW.html