1
|
Zhang Q, Lahiri SN, Nordman DJ. On optimal block resampling for Gaussian-subordinated long-range dependent processes. Ann Stat 2022. [DOI: 10.1214/22-aos2242] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Qihao Zhang
- Department of Statistics, Iowa State University
| | - Soumendra N. Lahiri
- Department of Mathematics and Statistics, Washington University in St. Louis
| | | |
Collapse
|
2
|
Renewal type bootstrap for increasing degree U-process of a Markov chain. J MULTIVARIATE ANAL 2022. [DOI: 10.1016/j.jmva.2022.105143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
|
3
|
Marinucci D, Rossi M, Vidotto A. Non-universal fluctuations of the empirical measure for isotropic stationary fields on S2×R. ANN APPL PROBAB 2021. [DOI: 10.1214/20-aap1648] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Domenico Marinucci
- Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”
| | - Maurizia Rossi
- Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca
| | - Anna Vidotto
- Dipartimento di Economia, Università degli Studi “G. D’Annunzio” Chieti-Pescara
| |
Collapse
|
4
|
Beran J, Steffens B, Ghosh S. Testing for the expected number of exceedances in strongly dependent seasonal time series. J Nonparametr Stat 2021. [DOI: 10.1080/10485252.2021.1977301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Jan Beran
- Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany
| | - Britta Steffens
- Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany
| | - Sucharita Ghosh
- Statistics Lab, Swiss Federal Research Institute WSL, Birmensdorf, Switzerland
| |
Collapse
|
5
|
Hidalgo J. Bootstrap long memory processes in the frequency domain. Ann Stat 2021. [DOI: 10.1214/20-aos2006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
6
|
Caron E, Dedecker J, Michel B. Gaussian linear model selection in a dependent context. Electron J Stat 2021. [DOI: 10.1214/21-ejs1885] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Emmanuel Caron
- Avignon Université, Laboratoire de Mathématiques d’Avignon EA2151, 84000 Avignon, France http://ecaron.perso.math.cnrs.fr/index.html
| | - Jérôme Dedecker
- Université de Paris, Laboratoire MAP5 UMR 8145, 75006 Paris, France http://w3.mi.parisdescartes.fr/~jdedecke/
| | - Bertrand Michel
- Ecole Centrale de Nantes, Laboratoire de Mathématiques Jean Leray UMR 6629, 44300 Nantes, France http://bertrand.michel.perso.math.cnrs.fr
| |
Collapse
|
7
|
Beran J, Sabzikar F, Surgailis D, Telkmann K. On the empirical process of tempered moving averages. Stat Probab Lett 2020. [DOI: 10.1016/j.spl.2020.108902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
8
|
Beran J, Telkmann K. On inference for modes under long memory. Scand Stat Theory Appl 2020. [DOI: 10.1111/sjos.12476] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
Affiliation(s)
- Jan Beran
- Department of Mathematics Statistics University of Konstanz Germany
| | | |
Collapse
|
9
|
Cammarota V, Marinucci D. A reduction principle for the critical values of random spherical harmonics. Stoch Process Their Appl 2020. [DOI: 10.1016/j.spa.2019.07.006] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
10
|
Shen Y, Han F, Witten D. Exponential inequalities for dependent V-statistics via random Fourier features. ELECTRON J PROBAB 2020. [DOI: 10.1214/20-ejp411] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
11
|
Guillotin-Plantard N, Pène F, Wendler M. Empirical processes for recurrent and transient random walks in random scenery. ESAIM-PROBAB STAT 2020. [DOI: 10.1051/ps/2019030] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
In this paper, we are interested in the asymptotic behaviour of the sequence of processes (Wn(s,t))s,t∈[0,1] with
\begin{equation*}
W_n(s,t):=\sum_{k=1}^{\lfloor nt\rfloor}\big(\mathds{1}_{\{\xi_{S_k}\leq s\}}-s\big)
\end{equation*}
where (ξx, x ∈ ℤd) is a sequence of independent random variables uniformly distributed on [0, 1] and (Sn)n ∈ ℕ is a random walk evolving in ℤd, independent of the ξ’s. In M. Wendler [Stoch. Process. Appl. 126 (2016) 2787–2799], the case where (Sn)n ∈ ℕ is a recurrent random walk in ℤ such that (n−1/αSn)n≥1 converges in distribution to a stable distribution of index α, with α ∈ (1, 2], has been investigated. Here, we consider the cases where (Sn)n ∈ ℕ is either:
(a) a transient random walk in ℤd,
(b) a recurrent random walk in ℤd such that (n−1/dSn)n≥1 converges in distribution to a stable distribution of index d ∈{1, 2}.
Collapse
|
12
|
A Note on Distributions in the Second Chaos. Symmetry (Basel) 2019. [DOI: 10.3390/sym11121487] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this article we study basic properties of random variables X, and their associated distributions, in the second chaos, meaning that X has a representation X = ∑ k ≥ 1 λ k ( ξ k 2 − 1 ) , where ξ k ∼ N ( 0 , 1 ) are independent. We compute the Lévy-Khintchine representations which we then use to study the smoothness of each density function. In particular, we prove the existence of a smooth density with asymptotically vanishing derivatives whenever λ k ≠ 0 infinitely often. Our work generalises some known results presented in the literature.
Collapse
|
13
|
Ghosh S. A note on using the empirical moment generating function to estimate the variance of nonparametric trend estimates from independent time series replicates. COMMUN STAT-SIMUL C 2018. [DOI: 10.1080/03610918.2018.1516291] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Sucharita Ghosh
- Swiss Federal Research Institute WSL, CH-8903 Birmensdorf, Switzerland
| |
Collapse
|
14
|
Beran J, Telkmann K. On nonparametric density estimation for multivariate linear long-memory processes. COMMUN STAT-THEOR M 2018. [DOI: 10.1080/03610926.2017.1395048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Jan Beran
- Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany
| | - Klaus Telkmann
- Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany
| |
Collapse
|
15
|
Cammarota V, Marinucci D. A quantitative central limit theorem for the Euler–Poincaré characteristic of random spherical eigenfunctions. ANN PROBAB 2018. [DOI: 10.1214/17-aop1245] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
16
|
Wu W, Zhou Z. Simultaneous quantile inference for non-stationary long-memory time series. BERNOULLI 2018. [DOI: 10.3150/17-bej951] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
17
|
Buchsteiner J. The function-indexed sequential empirical process under long-range dependence. BERNOULLI 2018. [DOI: 10.3150/17-bej924] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
18
|
Radulović D, Wegkamp M. Weak convergence of stationary empirical processes. J Stat Plan Inference 2018. [DOI: 10.1016/j.jspi.2017.09.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
19
|
Bai S, Taqqu MS. How the Instability of Ranks Under Long Memory Affects Large-Sample Inference. Stat Sci 2018. [DOI: 10.1214/17-sts633] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
20
|
|
21
|
Ghosh S. On estimating the marginal distribution of a detrended series with long memory. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2016.1275698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Sucharita Ghosh
- Statistics Lab, Swiss Federal Research Institute WSL, Birmensdorf, Switzerland
| |
Collapse
|
22
|
|
23
|
Beran J, Schumm N. On non parametric statistical inference for densities under long-range dependence. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2016.1263740] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Jan Beran
- Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany
| | - Nadja Schumm
- Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany
| |
Collapse
|
24
|
Functional central limit theorems for the Nelson–Aalen and Kaplan–Meier estimators for dependent stationary data. Stat Probab Lett 2017. [DOI: 10.1016/j.spl.2017.01.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
25
|
Dehling H, Rooch A, Wendler M. Two-sample U-statistic processes for long-range dependent data. STATISTICS-ABINGDON 2017. [DOI: 10.1080/02331888.2016.1270542] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- H. Dehling
- Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany
| | - A. Rooch
- Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany
| | - M. Wendler
- Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität, Greifswald, Germany
| |
Collapse
|
26
|
Franke B, Pène F, Wendler M. Stable limit theorem for $U$-statistic processes indexed by a random walk. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2017. [DOI: 10.1214/16-ecp4173] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
27
|
Betken A. Change point estimation based on Wilcoxon tests in the presence of long-range dependence. Electron J Stat 2017. [DOI: 10.1214/17-ejs1323] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
28
|
Tewes J. Change-point tests under local alternatives for long-range dependent processes. Electron J Stat 2017. [DOI: 10.1214/17-ejs1285] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
29
|
Dehling H, Rooch A, Taqqu MS. Power of change-point tests for long-range dependent data. Electron J Stat 2017. [DOI: 10.1214/17-ejs1283] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
30
|
Asymptotics for random functions moderated by dependent noise. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2016. [DOI: 10.1007/s11203-015-9130-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
31
|
Wendler M. The sequential empirical process of a random walk in random scenery. Stoch Process Their Appl 2016. [DOI: 10.1016/j.spa.2016.03.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
32
|
Beran J, Möhrle S, Ghosh S. Testing for Hermite Rank in Gaussian Subordination Processes. J Comput Graph Stat 2016. [DOI: 10.1080/10618600.2015.1056345] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
33
|
Davydov Y, Zitikis R. Generalized Lorenz curves and convexifications of stochastic processes. J Appl Probab 2016. [DOI: 10.1239/jap/1067436090] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We investigate convex rearrangements, called convexifications for brevity, of stochastic processes over fixed time intervals and develop the corresponding asymptotic theory when the time intervals indefinitely expand. In particular, we obtain strong and weak limit theorems for these convexifications when the processes are Gaussian with stationary increments and then illustrate the results using fractional Brownian motion. As a theoretical basis for these investigations, we extend some known, and also obtain new, results concerning the large sample asymptotic theory for the empirical generalized Lorenz curves and the Vervaat process when observations are stationary and either short-range or long-range dependent.
Collapse
|
34
|
Abstract
We investigate convex rearrangements, called convexifications for brevity, of stochastic processes over fixed time intervals and develop the corresponding asymptotic theory when the time intervals indefinitely expand. In particular, we obtain strong and weak limit theorems for these convexifications when the processes are Gaussian with stationary increments and then illustrate the results using fractional Brownian motion. As a theoretical basis for these investigations, we extend some known, and also obtain new, results concerning the large sample asymptotic theory for the empirical generalized Lorenz curves and the Vervaat process when observations are stationary and either short-range or long-range dependent.
Collapse
|
35
|
Delattre S, Roquain E. On empirical distribution function of high-dimensional Gaussian vector components with an application to multiple testing. BERNOULLI 2016. [DOI: 10.3150/14-bej659] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
36
|
Ghosh S. Computation of Spatial Gini Coefficients. COMMUN STAT-THEOR M 2015. [DOI: 10.1080/03610926.2013.823211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
37
|
Taufer E. On the empirical process of strongly dependent stable random variables: asymptotic properties, simulation and applications. Stat Probab Lett 2015. [DOI: 10.1016/j.spl.2015.07.032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
38
|
Cammarota V, Marinucci D. On the limiting behaviour of needlets polyspectra. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2015. [DOI: 10.1214/14-aihp609] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
39
|
Dedecker J, Dehling H, Taqqu MS. Weak convergence of the empirical process of intermittent maps in 𝕃2 under long-range dependence. STOCH DYNAM 2015. [DOI: 10.1142/s0219493715500082] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We study the behavior of the empirical distribution function of iterates of intermittent maps in the Hilbert space of square integrable functions with respect to Lebesgue measure. In the long-range dependent case, we prove that the empirical distribution function, suitably normalized, converges to a degenerate stable process, and we give the corresponding almost sure result. We apply the results to the convergence of the Wasserstein distance between the empirical measure and the invariant measure. We also apply it to obtain the asymptotic distribution of the corresponding Cramér–von-Mises statistic.
Collapse
Affiliation(s)
- Jérôme Dedecker
- Université Paris Descartes, Sorbonne Paris Cité, Laboratoire MAP5 and CNRS UMR 8145, 75016 Paris, France
| | - Herold Dehling
- Faculty of Mathematics, Ruhr-University Bochum, 44780 Bochum, Germany
| | - Murad S. Taqqu
- Department of Mathematics, Boston University, Boston, MA 02215, USA
| |
Collapse
|
40
|
|
41
|
|
42
|
Podolskij M, Schmidt C, Ziegel JF. Limit theorems for nondegenerate U-statistics of continuous semimartingales. ANN APPL PROBAB 2014. [DOI: 10.1214/13-aap983] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
43
|
|
44
|
|
45
|
Beutner E, Zähle H. Continuous mapping approach to the asymptotics of $U$- and $V$-statistics. BERNOULLI 2014. [DOI: 10.3150/13-bej508] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
46
|
Zhou Z. Inference of weighted $V$-statistics for nonstationary time series and its applications. Ann Stat 2014. [DOI: 10.1214/13-aos1184] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
47
|
Volgushev S, Shao X. A general approach to the joint asymptotic analysis of statistics from sub-samples. Electron J Stat 2014. [DOI: 10.1214/14-ejs888] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
48
|
Dehling H, Durieu O, Tusche M. A sequential empirical CLT for multiple mixing processes with application to $\mathcal{B}$-geometrically ergodic Markov chains. ELECTRON J PROBAB 2014. [DOI: 10.1214/ejp.v19-3216] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
49
|
|
50
|
Menéndez P, Ghosh S, Künsch HR, Tinner W. On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series. J Nonparametr Stat 2013. [DOI: 10.1080/10485252.2013.826357] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|