riecovest.distance.tyler_log_likelihood_no_normalization

riecovest.distance.tyler_log_likelihood_no_normalization(data, cov)

Log likelihood function for a complex elliptically symmetric distribution.

Same as tyler_log_likelihood, but without normalizing the data to be unit vectors.

It is not a true likelihood, since the mass is not 1. It is however proportional to true likelihood with regards to the covariance matrix. Anything constant with regards to the covariance is not taken into account. Therefore, the maximum likelihood estimator can be found by maximizing this function.

Parameters:

• data (ndarray of shape (dim, num_samples)) – data matrix that the likelihood is computed for

• cov (ndrray of shape (dim, dim)) – Covariance matrix of the distibution

Returns:

likelihood – The log likelihood of the data given the covariance matrix

Return type:

float

References

[ollilaComplex2012] E. Ollila, D. E. Tyler, V. Koivunen, and H. V. Poor, “Complex elliptically symmetric distributions: survey, new results and applications,” IEEE Transactions on Signal Processing, vol. 60, no. 11, pp. 5597–5625, Nov. 2012, doi: 10.1109/TSP.2012.2212433.