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:

Introduced in 2012
 (9.0)