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

Yoichi Nishiyama

doi:10.1016/j.spa.2007.07.011

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

Yoichi Nishiyama^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Pages (from-to)	1043-1055
Number of pages	13
Journal	Stochastic Processes and their Applications
Volume	118
Issue number	6
DOIs	https://doi.org/10.1016/j.spa.2007.07.011
Publication status	Published - 2008 Jun
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1016/j.spa.2007.07.011

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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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SN - 0304-4149

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SP - 1043

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 6

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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