Nancy Reid is University Professor in the Department of Statistical Sciences at the University of Toronto. Her research interests include statistical theory, likelihood inference, design of studies, and statistical science in public policy. She is a former President of the IMS, and is President-Elect of the Bernoulli Society. Nancy was the COPSS Distinguished Achievement Award Lecturer at JSM 2022. She is a Fellow of the ASA and IMS, and a Foreign Associate of the National Academy of Sciences. The IMS Grace Wahba Lecture will be given at the Joint Statistical Meetings in Portland, Oregon.

Models and Parameters: Inference under model misspecification

Parametric models for statistical inference are often very helpful for isolating particular features of the system under study, even if the model is at best an idealized abstraction. Inference for sufficiently well-behaved parametric models is relatively straightforward, and often has the advantage of providing interpretable conclusions.

However, the choice of a model and parametrization that allows for incisive conclusions is more difficult than it may seem. Even the meaning of a parameter may not be straightforward, a point emphasized in McCullagh (2002). One solution is to use methods that give valid conclusions with minimal model assumptions, although this may come at the expense of relevance or interpretability. Another is to identify stable estimands under a wide range of models, and target estimation on these parameters, as in, for example Vansteelandt & Dukes (2022). Inference derived from some forms of composite likelihood has a similar flavour, as does the development of doubly-robust estimators of causal effects.

In this talk we consider inference for a parameter of interest, in models that share a common interpretation for that parameter but that may differ appreciably in other respects. We study the general structure of models for which the maximum likelihood estimator of the parameter of interest is consistent, under arbitrary misspecification of the nuisance part of the model. A specialization of the general results to matched-comparison and two-groups problems gives a more explicit condition in terms of a new notion of symmetric parametrization. This generalizes a result derived in Battey & Cox (2020), and sheds light on the role of orthogonal parametrizations.

The work is joint with Heather Battey, Imperial College London.