Asymptotic inference for semimartingale models with singular parameter points
type: Item
instance of: scholarly article
title: Asymptotic inference for semimartingale models with singular parameter points
zbMATH Open document ID: 0807.62062
DOI: 10.1016/0378-3758(94)90204-6
author: Harald Luschgy
published in: Journal of Statistical Planning and Inference
publication date: 1994-07-12T00:00:00Z
review text: The author studies the asymptotic inference for stochastic processes using semimartingale models. In particular he discusses singularities in the parameter space. The paper clarifies some of the reasons for singular points for differentiable experiments in this context. The basic setup is the following: the law of the semimartingale depends on a \(k\)-dimensional Euclidean parameter \(\vartheta\) in such a way that the triplet of the local characteristics, which depends on the unknown parameter \(\vartheta\), is differentiable, and so the score martingale exists. Using the predictable bracket of the score martingale the author derives a local quadratic approximation for the likelihood. With the help of this approximation he then studies singularity points in the parameter space. He then gives a criterion for the quadratic approximation to be mixed normal (and then there is no singularity at this point). This criterion is also based on the bracket of the score martingale. Next he studies the limiting distributions of certain estimators. The paper ends with examples dealing with continuous diffusion processes, diffusions with jumps and point processes. Since the author works with quasi-left continuous semimartingales, the results obtained cannot be applied to discrete time models.
reviewed by: Esko Valkeila
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62M09
Mathematics Subject Classification ID: 60G48
zbMATH DE Number: 605310
zbMATH Keywords: asymptotic inference
zbMATH Keywords: semimartingale models
zbMATH Keywords: singularities
zbMATH Keywords: differentiable experiments
zbMATH Keywords: score martingale
zbMATH Keywords: predictable bracket
zbMATH Keywords: local quadratic approximation
zbMATH Keywords: mixed normal
zbMATH Keywords: limiting distributions
zbMATH Keywords: continuous diffusion processes
zbMATH Keywords: diffusions with jumps
zbMATH Keywords: point processes
zbMATH Keywords: quasi-left continuous semimartingales
MaRDI profile type: Publication
full work available at URL: 0378-3758(94)90204-6
OpenAlex ID: W2042865985
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description: scientific article; zbMATH DE number 605310