Long-range dependence

We study the models and statistical inference theory for stochastic processes and random fields with long-range dependence: linear and non-linear regression models with long-range dependence, parametric and semi-parametric estimation of parameters, minimum contrast method of estimation parameters in spectral domain, statistical inference using higher-order information, asymptotic optimal designs under long-range dependence error structure, among the others.

Cardiff Investigators

• Prof. Nikolai Leonenko
• Prof. Anatoly Zhigljavsky

Collaborators

Prof. Ole Barndorff-Nielsen, Prof. Holger Dette, Prof. Wojbor Woyczynski, Prof. Alexander Ivanov, Prof. Vo Anh, Dr. Andrey Pepelishev, Dr. Ludmila Sakhno, Dr. Emanuele Taufer, Dr. Elina Moldavskaya, Dr. Michail Sharapov, Dr. A.H. El-Bassiouny, Dr. Vippal Savani

Selected publications

• Dette, H., Leonenko, N.N., Pepelyshev, A., Zhigljavsky, A. (2009) Asymptotic optimal designs under long-range dependence error structure, Bernoulli, 15, N4, 1036-1056, Corrections, Bernoulli (2012).
• Taufer, E., Leonenko, N.N. (2009) Simulation of Levy-driven Ornstein-Uhlenbeck processes with given marginal distribution, Computational Statistics and Data Analysis, 53, 2427-2437
• Ivanov, A.V., Leonenko, N.N. (2008) Semiparametric analysis of long-range dependence in nonlinear regression, J. Statist. Plann. Inference, 138, 1733-1753
• Anh, V.V., Leonenko, N.N., Sakhno, L.M. (2007) Statistical inference using higher-order information, J. Multivariate Analysis, 98, N4, 706-742
• Anh, V.V., Leonenko, N.N., Sakhno, L.M. (2007) Statistical inference based on the information of the second and third order, J. Statist. Plann. Inference, 137, 1302-1331
• Leonenko, N.N., Savani, V., Zhigljavsky, A., (2007), Autoregressive Negative Binomial processes, Les Annales de l`I.S.U.P. , vol. 51, Fasc. 1-2, 25-47
• Leonenko, N.N., Sakhno, L.M.(2006) On the Whittle estimators for some classes of continuous parameter random processes and fields, Staistics and Probability Letters, 76, 781-795
• Barndorff-Nielsen, O.E., Leonenko, N.N.(2005) Spectral properties of superpositions of Ornstein-Uhlenbeck type processes, Methodology and Computing in Applied Probability, 7, 335-352
• Anh, V.V., Leonenko, N.N., Sakhno, L.M., (2004), Quasi-likelihood-based higher-order spectral estimation of random fields with possible long-range dependence. Stochastic methods and their applications. J. Appl. Probab. 41A, 35-53
• Anh, V.V., Leonenko, N.N., Sakhno, L.M., (2004) On a class of minimum contrast estimators for fractional stochastic processes and fields. J. Statist. Plann. Inference 123, N 1, 161-185
• Ivanov, A.V., Leonenko, N.N. (2004) Asymptotic theory of nonlinear regression with long-range dependence. Math. Methods Statist. 13, N 2, 153-178
• Anh, V.V., Leonenko, N.N., Moldavskaya, E.M., Sakhno, L.M., (2003), Estimation of spectral densities with multiplicative parameter. Acta Appl. Math. 79, N 1-2, 115-128
• Leonenko, N.N., Woyczynski, W.A. (2001) Parameter identification for stochastic Burgers' flows via parabolic rescaling. Probab. Math. Statist. 21 (2001), no. 1, Acta Univ. Wrotslav. No. 2298, 1-55
• Leonenko, N.N., Taufer, E. (2001)Asymptotic properties of LSE in multivariate continuous regression with long memory stationary errors. Metron 59 (2001), no. 1-2, 55-72
• Leonenko, N.N., Sharapov, M.M., El-Bassiouny, A. H. On the exactness of normal approximation of LSE of regression coefficient of long-memory random fields. Statist. Probab. Lett. 48 (2000), no. 2, 121-126
• Leonenko, N.N., Sakhno, L.M. On the Kaplan-Meier estimator of long-range dependent sequences. Stat. Inference Stoch. Process. 4 (2001), no. 1, 17-40
• Leonenko, N.N., Woyczynski, W.A. (1999) Parameter identification for singular random fields arising in Burgers' turbulence. J. Statist. Plann. Inference 80 (1999), no. 1-2, 1-13
• Ivanov, A.V., Leonenko, N.N. (1989), Statistical Analysis of Random Fields, Mathematics and its Applications, 28. Kluwer Academic Publishers, Dordrecht/Boston/London