A unified approach to calculation of information operators in semiparametric models

2018/10/15 by Lu Mao, Mao, Lu
Computer Science · Mathematics · #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1810.06138

openalex publication_date 2018/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Cox's Regression Model for Counting Processes: A Large Sample Study
• Asymptotic Theory for the Frailty Model

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