Consider a noisy observation <tex>$Y=X+N$</tex> where <tex>$X$</tex> is a random variable, and <tex>$N$</tex> is a Gaussian random variable with zero mean, variance <tex>$\sigma^{2}$</tex>, independent from <tex>$X$</tex>. The object of this work is to construct a consistent estimator for the conditional cumulants of the random variable <tex>$X$</tex> given the observation <tex>$Y=y$</tex>, 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
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