Estimation of parameters for discretely observed diffusion processes with a variety of rates for information

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5 Citations (Scopus)

Abstract

A specific form of stochastic differential equation with unknown parameters are considered. We do not necessarily assume ergodicity or recurrency, and any moment conditions for the true process, but some tightness conditions for an information-like quantity. The interest is to estimate the parameters from discrete observations the step size of which tends to zero. Consistency and the rate of convergence of proposed estimators are presented. The rate is deduced naturally from the rate for the information-like quantities.

Original languageEnglish
Pages (from-to)545-575
Number of pages31
JournalAnnals of the Institute of Statistical Mathematics
Volume64
Issue number3
DOIs
Publication statusPublished - 2012 Jun
Externally publishedYes

Fingerprint

Diffusion Process
Discrete Observations
Moment Conditions
Tightness
Ergodicity
Unknown Parameters
Stochastic Equations
Rate of Convergence
Tend
Differential equation
Estimator
Zero
Estimate
Form

Keywords

  • Consistency
  • Discrete observations
  • Non-ergodic diffusions
  • Normalized information
  • Parametric inference
  • Rates of convergence

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

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abstract = "A specific form of stochastic differential equation with unknown parameters are considered. We do not necessarily assume ergodicity or recurrency, and any moment conditions for the true process, but some tightness conditions for an information-like quantity. The interest is to estimate the parameters from discrete observations the step size of which tends to zero. Consistency and the rate of convergence of proposed estimators are presented. The rate is deduced naturally from the rate for the information-like quantities.",
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AB - A specific form of stochastic differential equation with unknown parameters are considered. We do not necessarily assume ergodicity or recurrency, and any moment conditions for the true process, but some tightness conditions for an information-like quantity. The interest is to estimate the parameters from discrete observations the step size of which tends to zero. Consistency and the rate of convergence of proposed estimators are presented. The rate is deduced naturally from the rate for the information-like quantities.

KW - Consistency

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KW - Non-ergodic diffusions

KW - Normalized information

KW - Parametric inference

KW - Rates of convergence

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