Topics in shrinkage estimation and in causal inference

In Part I Shrinkage Estimation, we let X ∼ Np(theta, sigma2I), where both theta and sigma2 are unknown. We consider estimation of 0 under squared error loss function. We develop sufficient conditions for prior density functions such that the corresponding generalized Bayes estimators for theta are admissible. These conditions are analogous to the sufficient conditions in Brown & Hwang (1982), but the solution there is only for the case when sigma2 is known. To illustrate how to select hierarchical priors, we also apply these sufficient conditions to a widely used hierarchical Bayes model proposed by Maruyama & Strawderman (2005), and obtain a class of admissible and minimax generalized Bayes estimators for the normal mean theta.;In Part II Causal Inference, we study the causal effect of winning an Oscar Award on an actor or actress's survival. Does the increase in social rank from a performer winning an Oscar increase the performer's life expectancy? Previous studies of this issue have suffered from survivor treatment selection bias, that is, candidates will have more chance to win Oscar Awards if they live longer, and winning an Oscar Award at a certain age is also an indicator of health status. To correct this bias, we adapt Robins' structural accelerated failure time model and g-estimation method. We show in simulation studies that this approach corrects the survivor treatment selection bias contained in previous studies. We estimate that the effect of winning an Oscar Award on survival is 4.2 years, with a 95% confidence interval of [-0.4, 8.4] years. There is not strong evidence that winning an Oscar increases life expectancy.