Bayesian estimation and prediction under a bounded asymmetric BLINEX loss function

The research summarized in this dissertation involves development of a new family of bounded asymmetric loss functions, which we call BLINEX, and its applications in Bayesian statistical inference. We first explore applications of BLINEX loss in Bayesian estimation. We prove the existence and uniqueness of Bayesian estimator under BLINEX and its various properties. Our findings on the admissibility of Bayesian estimation under the BLINEX loss confirms the importance of loss structure specification, and are consistent with those obtained by Zellner when the LINEX loss is considered. Loss robustness under BLINEX loss is also discussed and conditions under which a BLINEX Bayesian estimate is epsilon-loss robust are provided. We also explore the potential applications of BLINEX loss in Bayesian prediction. We prove the existence of Bayesian predictor under BLINEX and provide strong numerical evidence to justify our conjecture that this Bayesian predictor is unique. A simulation example of direct mail marketing is provided to illustrate how Bayesian estimation under BLINEX can be used to improve real business decision problems.