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.
Dr Paul Zivich, University of North Carolina at Chapel Hill
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