Exact Confidence Intervals of the Extended Orey Index for Gaussian Processes

被引：1

作者：

Kubilius, Kestutis ^{[1
]}

Melichov, Dmitrij ^{[2
]}

机构：

[1] Vilnius Univ, Inst Math & Informat, Akad 4, LT-08663 Vilnius, Lithuania

[2] Vilnius Gediminas Tech Univ, Sauletekio Al 11, LT-10223 Vilnius, Lithuania

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2016年 / 18卷 / 03期

关键词：

Concentration inequality; Confidence intervals; Gaussian processes with the Orey index; Fractional Ornstein-Uhlenbeck process; Sub-fractional Brownian motion; FRACTIONAL BROWNIAN-MOTION; QUADRATIC VARIATIONS;

D O I：

10.1007/s11009-015-9460-9

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：

In this paper exact confidence intervals for the Orey index of Gaussian processes are obtained using concentration inequalities for Gaussian quadratic forms and discrete observations of the underlying process. The obtained result is applied to Gaussian processes with the Orey index which not necessarily have stationary increments.

引用

页码：785 / 804

页数：20

共 17 条

[1] [Anonymous], 2005, Electronic Journal of Probability
[2] Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes
Begyn, Arnaud
[J]. BERNOULLI, 2007, 13 (03) : 712 - 753
[3] Identification of filtered white noises
Benassi, A
Cohen, S
Istas, J
Jaffard, S
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1998, 75 (01) : 31 - 49
[4] Sub-fractional Brownian motion and its relation to occupation times
Bojdecki, T
Gorostiza, LG
Talarczyk, A
[J]. STATISTICS & PROBABILITY LETTERS, 2004, 69 (04) : 405 - 419
[5] Breton J.-C., 2012, Stat Inference Stoch Pocess, V15, P1
[6] Exact confidence intervals for the Hurst parameter of a fractional Brownian motion
Breton, Jean-Christophe
Nourdin, Ivan
Peccati, Giovanni
[J]. ELECTRONIC JOURNAL OF STATISTICS, 2009, 3 : 416 - 425
[7] Cheridito P., 2003, ELECTRON J PROBAB, V8, P1
[8] Coeurjolly J-F., 2001, Stat. Inference for Stoch. Proc, V4, P199, DOI [DOI 10.1023/A:1017507306245, 10.1023/A:1017507306245]
[9] Gladysev E. G., 1961, Teor. Verojatnost. i Primenen., V6, P57
[10] GUYON X, 1989, ANN I H POINCARE-PR, V25, P265

← 1 2 →