Bayesian estimation and posterior risk under the generalized weighted squared error loss function and its applications

This paper proposed a new family of loss function, as a generalization of weighted squared error loss function, aiming to construct more new loss functions. We proposed the definition of the generalized weighted squared error loss function and derived the Bayesian estimation and its posterior risk under the generalized weighted squared error loss function based on the definition. Moreover, some members of the family of the generalized weighted squared error loss function are discussed. The results show that the proposed generalized weighted squared error loss function contains some existing loss functions in special cases and can obviously be employed to generate more new ones. The expressions of Bayesian estimations and their posterior risks of Rayleigh distribution parameter under the squared error loss function, weighted squared-negative exponential error loss function and LINEX loss function are derived respectively. For ease of explanation, Monte Carlo simulation example and application example are provided, and the results are compared based on posterior risk.