Consistent Estimation of Conditional Cumulants in the Empirical Bayes Framework (Extended Abstract)

Consider a noisy observation
$Y=X+N$
where
$X$
is a random variable, and
$N$
is a Gaussian random variable with zero mean, variance
$\sigma^{2}$
, independent from
$X$
. The object of this work is to construct a consistent estimator for the conditional cumulants of the random variable
$X$
given the observation
$Y=y$
, in the empirical Bayes framework. Cu-mulants are important statistical quantities that provide useful alternatives to moments and have a variety of applications [1]–[4]. Given the conditional cumulant generating function