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The asymptotic decision theory by Le Cam and Hajek has been given a lucidperspective by the Ibragimov-Hasminskii theory on convergence of the likelihoodrandom field. Their scheme has been applied to stochastic processes byKutoyants, and today this plot is called the IHK program. This scheme ensuresthat asymptotic properties of an estimator follow directly from the convergenceof the random field if a large deviation estimate exists. The quasi-likelihoodanalysis (QLA) proved a polynomial type large deviation (PLD) inequality to gothrough a bottleneck of the program. A conclusion of the QLA is that if thequasi-likelihood random field is asymptotically quadratic and if a key indexreflecting identifiability the random field has is non-degenerate, then the PLDinequality is always valid, and as a result, the IHK program can run. Manystudies already took advantage of the QLA theory. However, not a few of themare using it in an inefficient way yet. The aim of this paper is to provide areformed and simplified version of the QLA and to improve accessibility to thetheory. As an example of the effects of the theory based on the PLD, the usercan obtain asymptotic properties of the quasi-Bayesian estimator by onlyverifying non-degeneracy of the key index.

Simplified quasi-likelihood analysis for a locally asymptotically quadratic random field