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

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  • Nishiyama, Yoichi

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[infinity]-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.

Suggested Citation

  • Nishiyama, Yoichi, 2008. "Nonparametric estimation and testing time-homogeneity for processes with independent increments," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 1043-1055, June.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:6:p:1043-1055
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    References listed on IDEAS

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    1. Sangyeol Lee & Yoichi Nishiyama & Nakahiro Yoshida, 2006. "Test for Parameter Change in Diffusion Processes by Cusum Statistics Based on One-step Estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 211-222, June.
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    Cited by:

    1. Shimizu, Yasutaka, 2009. "Functional estimation for Lvy measures of semimartingales with Poissonian jumps," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1073-1092, July.

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