M-estimation
M-estimation, originally developed to study the large sample properties of robust statistics, is a general statistical approach that simplifies and unifies estimation. In particular, M-estimation allows for stacked estimating equations (possibly consisting of both interest and nuisance parameters) to be estimated simultaneously. While M-estimation simplifies the analysis of asymptotic behaviour of estimators, it also provides straightforward point and variance estimators. Recently, software that implements M-estimators given user-specified estimating equations has reduced barriers to the use of M-estimators.
To highlight the applicability of M-estimators to a variety of problems, we review examples in regression, dose-response relationships, causal inference, and transportability of randomised trials. Each example is illustrated with the corresponding estimation equations, data and computer code.
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, University of North Carolina at Chapel Hill
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