$M_j=\left\{P\left(y\mathrm{<mo>\; |\; </mo>}{\theta }_j\right)\mathrm{<mo>\; :\; </mo>}{\theta }_j\in {\Theta }_j\right\}$ ,

Different models(each is a set of density)

$K\left(x\mathrm{,}y\right)$

The Kullback-Leibler distance between x, y

${\mathcal{l}}_j\left({\theta }_j\right)$

the log-likelihood function for model j

${\widehat{P}}_j\left(y\right)=P\left(y\mathrm{<mo>\; |\; </mo>}{\widehat{\theta }}_j\right)$

An estimate of P based on model j

$d_j$

The dimension of ${\Theta }_j$

$Y_j$

The Data drawn from density P

${\widehat{\theta }}_j$

The MLE of model j

$s\left(y\mathrm{<mo>\; |\; </mo>}{\theta }_j\right)=\frac{\partial \log P\left(y\mathrm{<mo>\; |\; </mo>}{\theta }_j\right)}{\partial {\theta }_j}$

The Jaccobi Matrix of log $P\left(y\mathrm{<mo>\; |\; </mo>}{\theta }_j\right)$