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