  The asymptotic decision theory by Le Cam and Hajek has been given a lucid
perspective by the Ibragimov-Hasminskii theory on convergence of the likelihood
random field. Their scheme has been applied to stochastic processes by
Kutoyants, and today this plot is called the IHK program. This scheme ensures
that asymptotic properties of an estimator follow directly from the convergence
of the random field if a large deviation estimate exists. The quasi-likelihood
analysis (QLA) proved a polynomial type large deviation (PLD) inequality to go
through a bottleneck of the program. A conclusion of the QLA is that if the
quasi-likelihood random field is asymptotically quadratic and if a key index
reflecting identifiability the random field has is non-degenerate, then the PLD
inequality is always valid, and as a result, the IHK program can run. Many
studies already took advantage of the QLA theory. However, not a few of them
are using it in an inefficient way yet. The aim of this paper is to provide a
reformed and simplified version of the QLA and to improve accessibility to the
theory. As an example of the effects of the theory based on the PLD, the user
can obtain asymptotic properties of the quasi-Bayesian estimator by only
verifying non-degeneracy of the key index.
