Electronic Journal of Statistics

Nadaraya-Watson estimator for stochastic processes driven by stable Lévy motions

Hongwei Long and Lianfen Qian

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 7 (2013), 1387-1418.

Dates
First available in Project Euclid: 10 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1368193536

Digital Object Identifier
doi:10.1214/13-EJS811

Mathematical Reviews number (MathSciNet)
MR3063612

Zentralblatt MATH identifier
1337.62204

Subjects
Primary: 62G20: Asymptotic properties 62M05: Markov processes: estimation
Secondary: 60G52: Stable processes 65C30: Stochastic differential and integral equations

Keywords
Central limit theorem consistency geometrically strong mixing kernel estimator Lévy motion Nadaraya-Watson estimator rate of convergence stable stochastic integrals

Citation

Long, Hongwei; Qian, Lianfen. Nadaraya-Watson estimator for stochastic processes driven by stable Lévy motions. Electron. J. Statist. 7 (2013), 1387--1418. doi:10.1214/13-EJS811. https://projecteuclid.org/euclid.ejs/1368193536


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