ABSTRACT
Assessment of the uncertainty of estimation of an optimal regime and its value is challenging because this is an inherently nonsmooth statistical problem. As a result of this feature, standard large sample theory approximations to the sampling distribution of an estimator fail, and thus specialized techniques for obtaining valid large sample approximations are required. Several of these approaches to obtaining valid statistical inference for treatment regimes in both the single and multiple decision settings are described. Not surprisingly, the material in this chapter is more technical than that in the rest of the book and may be of interest primarily to readers seeking an understanding of the theoretical underpinnings. Readers interested in achieving a basic appreciation of the challenges of statistical inference in nonsmooth problems will benefit from reviewing the first two sections of the chapter.
