Inferential Models

234 FUTURE RESEARCH TOPICS

framework’s ability to handle partial prior information will help to push it into the

statistical mainstream. We propose to call this general idea partial- or semi-Bayes.

12.2.7 Nonparametric problems

By nonparametric, here we mean those problems where the parameter of interest

is infinite-dimensional, i.e., θ is a function rather than a number or vector. For ex-

ample, θ could be the density function itself or perhaps a regression function. Re-

search in this direction has focused primarily on producing estimators of the infinite-

dimensional parameter and studying the estimator’s convergence properties. While

there has been some interest in recent literature on the construction of confidence

bands for θ, work on valid probabilistic ...