What are the regularity conditions for quasi-maximum likelihood estimators?

Question

What are the regularity conditions for Quasi-Maximum Likelihood Estimators (QMLE)?¹ Could you advise me a good book where I can find detailed proofs?

_{1. For example, regularity conditions for MLE are discussed here (pdf).}

Answer 1

See

White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica, Vol. 50, No. 1 (Jan., 1982), pp. 1-25

As with most of the late H. White's work, it is very detailed and rigorous on the "assumptions and regularity conditions" fronts. And it is essentially the first paper that treated the QMLE so formally.