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2013 Nadaraya-Watson estimator for stochastic processes driven by stable Lévy motions
Hongwei Long, Lianfen Qian
Electron. J. Statist. 7: 1387-1418 (2013). DOI: 10.1214/13-EJS811

Abstract

We discuss the nonparametric Nadaraya-Watson (N-W) estimator of the drift function for ergodic stochastic processes driven by $\alpha$-stable noises and observed at discrete instants. Under geometrical mixing condition, we derive consistency and rate of convergence of the N-W estimator of the drift function. Furthermore, we obtain a central limit theorem for stable stochastic integrals. The central limit theorem has its own interest and is the crucial tool for the proofs. A simulation study illustrates the finite sample properties of the N-W estimator.

Citation

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Hongwei Long. Lianfen Qian. "Nadaraya-Watson estimator for stochastic processes driven by stable Lévy motions." Electron. J. Statist. 7 1387 - 1418, 2013. https://doi.org/10.1214/13-EJS811

Information

Published: 2013
First available in Project Euclid: 10 May 2013

zbMATH: 1337.62204
MathSciNet: MR3063612
Digital Object Identifier: 10.1214/13-EJS811

Subjects:
Primary: 62G20, 62M05
Secondary: 60G52, 65C30

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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