Fitting the exogenous model to measured data

The authors deal with the problem of fitting a statistical model to observations. The proposed approach relies on modeling data as drawn from an exogenous process, namely, a doubly stochastic random sequence, where a real non-negative process modulates a Gaussian, possibly complex, one. It is demonstrated that the problem of ascertaining to what extent the proposed model applies can be posed as a binary hypothesis testing problem; in particular, proper data processing leads to a distribution-free test statistic which is one and the same independent of the data distribution and correlation. The proposed procedure is validated where the operation characteristics of the test are evaluated with reference to a properly designed experimental setup