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Lin, Zhengyan; Song, Yuping; Yi, Jiangsheng

Local linear estimator for stochastic differential equations driven by \(\alpha\)-stable Lévy motions. (English) Zbl 1396.62064

Sci. China, Math. 57, No. 3, 609-626 (2014).
Summary: We study the local linear estimator for the drift coefficient of stochastic differential equations driven by \(\alpha\)-stable Lévy motions observed at discrete instants. Under regular conditions, we derive the weak consistency and central limit theorem of the estimator. Compared with Nadaraya-Watson estimator, the local linear estimator has a bias reduction whether the kernel function is symmetric or not under different schemes. A simulation study demonstrates that the local linear estimator performs better than Nadaraya-Watson estimator, especially on the boundary.

Cited in 4 Documents

MSC:

62G05 Nonparametric estimation
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
62G20 Asymptotic properties of nonparametric inference
62M05 Markov processes: estimation; hidden Markov models
65C30 Numerical solutions to stochastic differential and integral equations

Keywords:

local linear estimator; stable Lévy motion; drift coefficient; bias reduction; consistency; central limit theorem

Software:

KernSmooth
Cite Review PDF
Full Text: DOI

References:

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