A unified approach to calculation of information operators in semiparametric models

Abstract: The infinite-dimensional information operator for the nuisance parameter plays a key role in semiparametric inference, as it is closely related to the regular estimability of the target parameter. Calculation of information operators has traditionally proceeded in a case-by-case manner and has easily entailed lengthy derivations with complicated arguments. We develop a unified framework for this task by exploiting commonality in the form of semiparametric likelihoods. The general formula allows one to derive information operators with simple calculus and, if necessary at all, a minimal amount of probabilistic evaluations. This streamlined approach shows its efficiency and versatility in application to a number of popular models in survival analysis, inverse problems, and missing data.