gives Wilks's for the matrices m1 and m2.
- 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 real‐valued matrices or vectors of equal length.
Examplesopen allclose all
Basic Examples (3)
Compute Wilks's for two matrices:
Wilks's for two vectors:
Wilks's for a matrix and a vector:
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: