Title

Simplified quasi-likelihood analysis for a locally asymptotically quadratic random field: Simplified quasi-likelihood analysis: N. Yoshida.

Authors

Yoshida, Nakahiro

Abstract

The IHK program is a general framework in asymptotic decision theory, introduced by Ibragimov and Hasminskii and extended to semimartingales by Kutoyants. The quasi-likelihood analysis (QLA) asserts that a polynomial type large deviation inequality is always valid if the quasi-likelihood random field is asymptotically quadratic and if a key index reflecting the identifiability is non-degenerate. As a result, following the IHK program, the QLA gives a way to inference for various nonlinear stochastic processes. This paper provides a reformed and simplified version of the QLA and improves accessibility to the theory. As an example of the advantages of the scheme, the user can obtain asymptotic properties of the quasi-Bayesian estimator by only verifying non-degeneracy of the key index.

Subjects

RANDOM fields; STOCHASTIC processes; DECISION theory; QUADRATIC fields; STATISTICS

Publication

Annals of the Institute of Statistical Mathematics, 2025, Vol 77, Issue 1, p1

ISSN

0020-3157

Publication type

Academic Journal

DOI

10.1007/s10463-024-00907-8