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Is there a good book on statistical model misspecification in general? It should cover, for example, the behavior of estimators (e.g., maximum likelihood) when the specified parametric family does not include the true underlying model (assuming at least a true model exists). Note that I'm not much interested in those goodness-of-fit tests which detect model misspecification. Instead I'm interested in something roughly like "Fitting a wrong model which is close to the true model, how close can the result be with respect to the true model?"

I don't have any specific question to address. I got interested in this topic purely out of curiosity. Since "all models are wrong, but some are useful" (George E. P. Box), how wrong models behave should be of general interest and worth treating by a monograph in my opinion. I tried to google but only found scattered papers or notes.

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    $\begingroup$ You should edit your post to be more specific. Define what "model misspecification" means to you. What problem are you thinking about that has led you to this investigation? $\endgroup$
    – Matthew Drury
    Commented May 5, 2015 at 2:58
  • $\begingroup$ @MatthewDrury Thanks for suggestion. I hope now it looks clearer. $\endgroup$
    – Uchiha
    Commented May 6, 2015 at 2:58

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Here are exactly the books you are looking for:

Twenty years later stands for Halbert White's paper on the general sorts of misspecifications in likelihood models. It is arguably more readable than the original Huber (1967) paper.

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  • $\begingroup$ Thanks!. Ideally I would like something not in the collection form. But this seems to be a very nice reference anyway! $\endgroup$
    – Uchiha
    Commented May 6, 2015 at 12:45
  • $\begingroup$ Unlike most edited volumes, this one does have a unifying topic that ties it up together. But Hal White published his own monograph on the topic, and you may want to check it out, too. $\endgroup$
    – StasK
    Commented May 6, 2015 at 14:56

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