Nonparametric estimation and testing time-homogeneity for processes with independent increments

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We consider a nonparametric estimation problem for the Lévy measure of time-inhomogeneous process with independent increments. We derive the functional asymptotic normality and efficiency, in an ℓ-space, of generalized Nelson-Aalen estimators. Also we propose some asymptotically distribution free tests for time-homogeneity of the Lévy measure. Our result is a fruit of the empirical process theory and the martingale theory.

Original languageEnglish
Pages (from-to)1043-1055
Number of pages13
JournalStochastic Processes and their Applications
Volume118
Issue number6
DOIs
Publication statusPublished - 2008 Jun
Externally publishedYes

Fingerprint

Nonparametric Testing
Processes with Independent Increments
Nonparametric Estimation
Fruits
Homogeneity
Nelson-Aalen Estimator
Distribution-free Test
Asymptotic Efficiency
Empirical Process
Testing
Fruit
Asymptotic Normality
Martingale
Nonparametric testing
Nonparametric estimation
Process theory
Estimator
Asymptotic efficiency
Empirical process
Asymptotic normality

Keywords

  • Change point problem
  • Empirical process
  • Lévy process
  • Martingale
  • Nonparametric estimation
  • Process with independent increments

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Mathematics(all)
  • Statistics and Probability
  • Modelling and Simulation

Cite this

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abstract = "We consider a nonparametric estimation problem for the L{\'e}vy measure of time-inhomogeneous process with independent increments. We derive the functional asymptotic normality and efficiency, in an ℓ∞-space, of generalized Nelson-Aalen estimators. Also we propose some asymptotically distribution free tests for time-homogeneity of the L{\'e}vy measure. Our result is a fruit of the empirical process theory and the martingale theory.",
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AB - We consider a nonparametric estimation problem for the Lévy measure of time-inhomogeneous process with independent increments. We derive the functional asymptotic normality and efficiency, in an ℓ∞-space, of generalized Nelson-Aalen estimators. Also we propose some asymptotically distribution free tests for time-homogeneity of the Lévy measure. Our result is a fruit of the empirical process theory and the martingale theory.

KW - Change point problem

KW - Empirical process

KW - Lévy process

KW - Martingale

KW - Nonparametric estimation

KW - Process with independent increments

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