Maximum likelihood estimator for the sub-fractional Brownian motion approximated by a random walk

被引：26

作者：

Kuang, Nenghui ^{[1
,2
]}

Xie, Huantian ^{[2
,3
]}

机构：

[1] Hunan Univ Sci & Technol, Sch Math & Comp Sci, Xiangtan 411201, Hunan, Peoples R China

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[3] Linyi Univ, Sch Sci, Linyi 276005, Shandong, Peoples R China

来源：

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2015年 / 67卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Maximum likelihood estimator; Sub-fractional Brownian motion; Random walk; PARAMETRIC-ESTIMATION; DRIVEN;

D O I：

10.1007/s10463-013-0439-4

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We estimate the drift parameter in a simple linear model driven by sub-fractional Brownian motion. We construct a maximum likelihood estimator (MLE) for the drift parameter by using a random walk approximation of the sub-fractional Brownian motion and study the asymptotic behaviors of the estimator. Simulations confirm the theoretical results and indicate superiority of the new proposed estimator.

引用

页码：75 / 91

页数：17

共 13 条

[1]

Bertin K., 2009, ARXIV07110513V2

[2] Drift parameter estimation in fractional diffusions driven by perturbed random walks [J].

Bertin, Karine ;

Torres, Soledad ;

Tudor, Ciprian A. .

STATISTICS & PROBABILITY LETTERS, 2011, 81 (02) :243-249

[3]

Billingsley P., 1999, CONVERGE PROBAB MEAS, V2nd, DOI DOI 10.1002/9780470316962

[4] Sub-fractional Brownian motion and its relation to occupation times [J].

Bojdecki, T ;

Gorostiza, LG ;

Talarczyk, A .

STATISTICS & PROBABILITY LETTERS, 2004, 69 (04) :405-419

[5]

Golub G.H., 2013, Matrix computations, V3

[6]

Kleptsyna M., 2002, STAT INFER STOCH PRO, V5, P229, DOI DOI 10.1023/A:1021220818545

[7] Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion [J].

Le Breton, A .

STATISTICS & PROBABILITY LETTERS, 1998, 38 (03) :263-274

[8] Parametric estimation for sub-fractional Ornstein-Uhlenbeck process [J].

Mendy, Ibrahima .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2013, 143 (04) :663-674

[9]

Prakasa Rao B. L. S., 1999, STAT INFERENCE DIFFU

[10] Parametric estimation for linear stochastic delay differential equations driven by fractional Brownian motion [J].

Rao, B. L. S. Prakasa .

RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2008, 16 (01) :27-38

← 1 2 →