# 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 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.

#### 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

#### BibTeX

@misc{reference.wolfram_2024_wilksw, author="Wolfram Research", title="{WilksW}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/WilksW.html}", note=[Accessed: 17-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_wilksw, organization={Wolfram Research}, title={WilksW}, year={2012}, url={https://reference.wolfram.com/language/ref/WilksW.html}, note=[Accessed: 17-July-2024 ]}