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Statistical inference for infinite-dimensional parameters via asymptotically pivotal estimating functions

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  • M. A. Goldwasser

Abstract

Suppose that a consistent estimator for an infinite-dimensional parameter can be readily obtained via a set of estimating functions which has a 'good' local linear approximation around the true value of the parameter. However, it may be difficult to estimate the variance function of this estimator well. We show that, if the set of estimating functions evaluated at the true parameter value is 'asymptotically pivotal', then the 'fiducial' distribution of the parameter can be used to approximate the distribution of this consistent estimator. We present three examples to illustrate that the corresponding inference for the parameter can be made via a simple simulation technique without involving complex, high-dimensional nonparametric density estimates. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • M. A. Goldwasser, 2004. "Statistical inference for infinite-dimensional parameters via asymptotically pivotal estimating functions," Biometrika, Biometrika Trust, vol. 91(1), pages 81-94, March.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:1:p:81-94
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    Cited by:

    1. Yuhyun Park & Lu Tian & L. J. Wei, 2004. "One- and Two-Sample Nonparametric Inference Procedures in the Presence of Dependent Censoring," Harvard University Biostatistics Working Paper Series 1012, Berkeley Electronic Press.
    2. Larry F. León & Ray Lin & Keaven M. Anderson, 2020. "On Weighted Log-Rank Combination Tests and Companion Cox Model Estimators," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(2), pages 225-245, July.

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