J-function Implementations

For analysis of this feature transformation we use the “energy statistic" (ES) approach of Section 3.2.2. However, for exponential data, the scale parameter is the mean, not the variance, so the energy statistic can be “built-in" to the feature without needing to add an explicit energy statistic.

There are three analysis tools for computing $J({\bf x})$, the saddlepoint approximation (SPA) (sections 17.6, 5.2.1, 2.3.2) the central limit theorem (CLT) (Section 5.2.4), and the maximum likelihood (ML) approach (Sections 2.3.5,5.2.7). We will compare all three approaches using the auto-regressive (AR) features in section 10.4.10.