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Abstract Details

Activity Number: 297
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
Sponsor: Biometrics Section
Abstract - #305426
Title: Estimating Infinite-Dimensional Parameters via Pointwise Estimation
Author(s): Marco Carone*+ and Mark van der Laan
Companies: University of California at Berkeley and University of California at Berkeley School of Public Health
Address: Division of Biostatistics, Berkeley, CA, 94720, United States
Keywords: infinite-dimensional parameter ; pointwise estimation ; targeted maximum likelihood estimation
Abstract:

Many important statistical tools are designed to estimate parameters of finite dimension. However, in many important applications, the statistical parameter lies in a space of infinite dimension; estimation of a survival function is a common example of such. In this work, we present a simple framework for constructing statistical procedures for estimating an infinite-dimensional parameter using estimators of its pointwise evaluation (a finite-dimensional parameter). We discuss the asymptotic properties of the resulting procedure, and we demonstrate how this approach, in conjunction with targeted maximum likelihood estimation, provides a formal framework for producing consistent and asymptotically efficient estimators of infinite-dimensional statistical parameters. We illustrate the merits of the approach through simulation studies.


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