Least squares estimator for α-sub-fractional bridges

被引：0

作者：

Kuang, Nenghui ^{[1
]}

Liu, Bingquan ^{[2
]}

机构：

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

[2] Weinan Normal Univ, Sch Math & Informat Sci, Weinan 714000, Peoples R China

来源：

STATISTICAL PAPERS | 2018年 / 59卷 / 03期

关键词：

Least squares estimator; Sub-fractional Brownian motion; alpha-sub-fractional bridge; ORNSTEIN-UHLENBECK PROCESS; BROWNIAN-MOTION; FUNCTIONALS; INTEGRATION; RESPECT; TIME;

D O I：

10.1007/s00362-016-0795-2

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：

Let alpha, T > 0. We investigate the asymptotic properties of a least squares estimator (LSE) for the parameter of alpha sub-fractional bridge defined as dX(t) = -alpha X-t/T-t dt + d S-t(H), O <= t < T, X-o = O, where S-H is a sub-fractional Brownian motion of Hurst parameter H is an element of(1/2, 1). Depending on the value of alpha, we prove that we may have strong consistency or not as t -> T. When we have consistency, we obtain the rate of this convergence as well.

引用

页码：893 / 912

页数：20

共 26 条

[1]

Alos A, 2003, STOCHASTICS STOCHAST, V75, P129

[2] Stochastic calculus with respect to Gaussian processes [J].

Alòs, E ;

Mazet, O ;

Nualart, D .

ANNALS OF PROBABILITY, 2001, 29 (02) :766-801

[3] Maximum likelihood estimation under a finite mixture of generalized exponential distributions based on censored data [J].

Ateya, Saieed F. .

STATISTICAL PAPERS, 2014, 55 (02) :311-325

[4] Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions [J].

Barczy, M. ;

Pap, G. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 380 (02) :405-424

[5] α-Wiener Bridges: Singularity of Induced Measures and Sample Path Properties [J].

Barczy, Matyas ;

Pap, Gyula .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2010, 28 (03) :447-466

[6] 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

[7]

Diedhiou A., 2011, J NUMERICAL MATH STO, V3, P37

[8]

Es-Sebaiy K, 2011, ARXIV11015790V2

[9] Parameter estimation for the non-stationary Ornstein-Uhlenbeck process with linear drift [J].

Jiang, Hui ;

Dong, Xing .

STATISTICAL PAPERS, 2015, 56 (01) :257-268

[10] Remarks on asymptotic behavior of weighted quadratic variation of subfractional Brownian motion [J].

Liu, Junfeng ;

Yan, Litan .

JOURNAL OF THE KOREAN STATISTICAL SOCIETY, 2012, 41 (02) :177-187

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