Nondegeneracy of Random Field and Estimation of Diffusion

2012/12/22 by Masayuki Uchida, Uchida, Masayuki, Nakahiro Yoshida +1
Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Approximation and Integration #Methodology (stat.ME) #NMR spectroscopy and applications #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.1212.5715

arxiv created 2012/12/22 · openalex publication_date 2012/12/22 · arxiv updated 2012/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a quasi likelihood analysis for diffusions under the high-frequency sampling over a finite time interval. For this, we prove a polynomial type large deviation inequality for the quasi likelihood random field. Then it becomes crucial to prove nondegeneracy of a key index chi₀. By nature of the sampling setting, chi₀ is random. This makes it difficult to apply a naive sufficient condition, and requires a new machinery. In order to establish a quasi likelihood analysis, we need quantitative estimate of the nondegeneracy of chi₀. The existence of a nondegenerate local section of a certain tensor bundle associated with the statistical random field solves this problem.

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