### Abstract

Let a one-dimensional ergodic diffusion process X be observed at time points 0 = t ^{n} _{0} < t ^{n} _{1} < ... < t ^{n} _{n} such that t ^{n} _{n} →∞ and n Δ ^{1+p} _{n} → 0, where Δ _{n} = max _{1≤i≤n}; {pipe}t ^{n} _{i} - t ^{n} _{i-1}{pipe}, with p ∈ (0, 1) being a constant depending also on some conditions on X. We consider the nonparametric estimation problems for the invariant distribution and the invariant density. In both problems, we propose some estimators which are asymptotically normal and asymptotically efficient in some functional senses.

Original language | English |
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Pages (from-to) | 909-915 |

Number of pages | 7 |

Journal | Journal of Nonparametric Statistics |

Volume | 23 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2011 Dec |

Externally published | Yes |

### Fingerprint

### Keywords

- Asymptotic efficiency
- Ergodic diffusion
- Invariant law
- Weak convergence

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**Estimation for the invariant law of an ergodic diffusion process based on high-frequency data.** / Nishiyama, Yoichi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Estimation for the invariant law of an ergodic diffusion process based on high-frequency data

AU - Nishiyama, Yoichi

PY - 2011/12

Y1 - 2011/12

N2 - Let a one-dimensional ergodic diffusion process X be observed at time points 0 = t n 0 < t n 1 < ... < t n n such that t n n →∞ and n Δ 1+p n → 0, where Δ n = max 1≤i≤n; {pipe}t n i - t n i-1{pipe}, with p ∈ (0, 1) being a constant depending also on some conditions on X. We consider the nonparametric estimation problems for the invariant distribution and the invariant density. In both problems, we propose some estimators which are asymptotically normal and asymptotically efficient in some functional senses.

AB - Let a one-dimensional ergodic diffusion process X be observed at time points 0 = t n 0 < t n 1 < ... < t n n such that t n n →∞ and n Δ 1+p n → 0, where Δ n = max 1≤i≤n; {pipe}t n i - t n i-1{pipe}, with p ∈ (0, 1) being a constant depending also on some conditions on X. We consider the nonparametric estimation problems for the invariant distribution and the invariant density. In both problems, we propose some estimators which are asymptotically normal and asymptotically efficient in some functional senses.

KW - Asymptotic efficiency

KW - Ergodic diffusion

KW - Invariant law

KW - Weak convergence

UR - http://www.scopus.com/inward/record.url?scp=84855717337&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855717337&partnerID=8YFLogxK

U2 - 10.1080/10485252.2011.591397

DO - 10.1080/10485252.2011.591397

M3 - Article

AN - SCOPUS:84855717337

VL - 23

SP - 909

EP - 915

JO - Journal of Nonparametric Statistics

JF - Journal of Nonparametric Statistics

SN - 1048-5252

IS - 4

ER -