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Estimating functions for repeated measures with incidental parameters

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Abstract

Repeated measures, or longitudinal data, are considered. The statistical characteristics for each individual case are supposed to be governed by a structural parameter, common to all, and an incidental parameter, specific to the individual. Introducing this terminology, Neyman and Scott studied the properties of estimators in a likelihood framework. In this paper the model specification is taken to be more limited, not sufficient to construct a proper likelihood function. The proposal here is to seek an estimating function, based on the data and the structural parameter alone, whose maximum has an identifiable limit as the sample size grows. Then a transformation of the maximum is sought so that the modified version is a consistent estimator. Some examples are worked through and asymptotic distributions of the resulting consistent estimators are outlined to enable tests and confidence regions to be derived. Relative efficiency of competing estimators is also considered.

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Authors and Affiliations

  1. Institute for Mathematical Sciences, Imperial College London, 53 Prince’s Gate, Exhibition Road, London, SW7 2PG, UK

    Martin Crowder

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  1. Martin Crowder
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Correspondence to Martin Crowder.

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Crowder, M. Estimating functions for repeated measures with incidental parameters. Ann Inst Stat Math 63, 535–558 (2011). https://doi.org/10.1007/s10463-009-0243-3

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  • DOI: https://doi.org/10.1007/s10463-009-0243-3

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