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On generalized moment identity and its applications: a unified approach
Authors:Sudheesh K Kattumannil  Isha Dewan
Institution:1. Department of Statistics and Probability, Michigan State University, Lansing, MI, USA;2. Indian Statistical Institute, Chennai, India;3. Indian Statistical Institute, New Delhi, India
Abstract:In this paper, we obtain a generalized moment identity for the case when the distributions of the random variables are not necessarily purely discrete or absolutely continuous. The proposed identity is useful to find the generator which has been used for the approximation of distributions by Stein's method. Apparently, a new approach is discussed for the approximation of distributions by Stein's method. We bring the characterization based on the relationship between conditional expectations and hazard measure in our unified framework. As an application, a new lower bound to the mean-squared error is obtained and it is compared with Bayesian Cramer–Rao bound.
Keywords:Bayesian Cramer–Rao bound  conditional variance  moment identity  reliability analysis  Stein's identity  unbiased estimation
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