文章基本信息

标题：Nadaraya-Watson estimator for stochastic processes driven by stable Lévy motions
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作者：Hongwei Long ; Lianfen Qian
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2013
卷号：7
页码：1387-1418
DOI：10.1214/13-EJS811
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.