Professor Anatoly Zhigljavsky

2025

• Scherbakova, I. et al., 2025. Statistical modelling for improving efficiency of online advertising. In: Aston, P. J. ed. More UK Success Stories in Industrial Mathematics. Mathematics in Industry Springer Nature Switzerland. , pp.205-211. (10.1007/978-3-031-48683-8_26)
• Wynn, H. P. and Zhigljavsky, A. 2025. An exterior algebra approach to generalised variances and cross-covariances. Soft Computing 29 (8), pp.4247-4257. (10.1007/s00500-025-10600-4)

2024

• Detter, H. , Pepelyshev, A. and Zhigljavsky, A. 2024. Prediction in regression models with continuous observations. Statistical Papers 65 , pp.1985-2009. (10.1007/s00362-023-01465-6)
• Noonan, J. and Zhigljavsky, A. 2024. Improving exploration strategies in large dimensions and rate of convergence of global random search algorithms. Journal of Global Optimization 88 , pp.1-26. (10.1007/s10898-023-01308-6)

2023

• Gillard, J. , O'Riordan, E. and Zhigljavsky, A. 2023. Polynomial whitening for high-dimensional data. Computational Statistics 38 , pp.1427-1461. (10.1007/s00180-022-01277-6)
• Pronzato, L. and Zhigljavsky, A. 2023. BLUE against OLSE in the location model: energy minimization and asymptotic considerations. Statistical Papers 64 , pp.1187-1208. (10.1007/s00362-023-01423-2)
• Pronzato, L. and Zhigljavsky, A. 2023. Quasi-uniform designs with optimal and near-optimal uniformity constant. Journal of Approximation Theory 294 105931. (10.1016/j.jat.2023.105931)

2022

• Gillard, J. , O'Riordan, E. and Zhigljavsky, A. 2022. Simplicial and minimal-variance distances in multivariate data analysis. Journal of Statistical Theory and Practice 16 9. (10.1007/s42519-021-00227-7)
• Noonan, J. and Zhigljavsky, A. 2022. Efficient quantisation and weak covering of high dimensional cubes. Discrete and Computational Geometry 68 , pp.540-565. (10.1007/s00454-022-00396-7)
• Noonan, J. and Zhigljavsky, A. 2022. Non-lattice covering and quantization of high dimensional sets. In: Pardalos, P. M. , Rasskazova, V. and Vrahatis, M. N. eds. Black Box Optimization, Machine Learning, and No-Free Lunch Theorems. Vol. 170, Springer Optimization and Its Applications New York: Springer. , pp.273-318. (10.1007/978-3-030-66515-9_10)
• Noonan, J. and Zhigljavsky, A. 2022. Random and quasi-random designs in group testing. Journal of Statistical Planning and Inference 221 , pp.29-54. (10.1016/j.jspi.2022.02.006)
• Zhigljavsky, A. 2022. Convergence of global random search algorithms. In: Pardalos, P. and Prokopyev, O. eds. Encylopedia of Optimization. Springer Nature. , pp.online. (10.1007/978-3-030-54621-2_769-1)
• Zhigljavsky, A. 2022. Random search for global optimization. In: Pardalos, P. and Prokopyev, O. eds. Encyclopedia of Optimization. Springer Nature. , pp.online. (10.1007/978-3-030-54621-2_768-1)
• Zhigljavsky, A. and Noonan, J. 2022. Covering of high-dimensional sets. In: Pardalos, P. and Prokopyev, O. eds. Encyclopedia of Optimization. Springer Nature. , pp.online. (10.1007/978-3-030-54621-2_770-1)

2021

• Dette, H. and Zhigljavsky, A. A. 2021. Reproducing kernel Hilbert spaces, polynomials, and the classical moment problem. SIAM/ASA Journal on Uncertainty Quantification 9 (4), pp.1589-1614. (10.1137/21M1394965)
• Noonan, J. and Zhigljavsky, A. 2021. Approximations for the boundary crossing probabilities of moving sums of normal random variables. Communications in Statistics - Simulation and Computation 50 (11), pp.3547-3568. (10.1080/03610918.2019.1626889)
• Noonan, J. and Zhigljavsky, A. 2021. Approximations for the boundary crossing probabilities of moving sums of random variables. Methodology and Computing in Applied Probability 23 , pp.873-892. (10.1007/s11009-019-09769-7)
• Pronzato, L. and Zhigljavsky, A. 2021. Minimum-energy measures for singular kernels. Journal of Computational and Applied Mathematics 382 113089. (10.1016/j.cam.2020.113089)
• Zhigljavsky, A. and Noonan, J. 2021. First passage times for Slepian process with linear and piecewise linear barriers. Extremes 24 , pp.565-589. (10.1007/s10687-021-00406-6)
• Zilinskas, A. et al., 2021. Multistart with early termination of descents. Journal of Global Optimization 79 , pp.447-462. (10.1007/s10898-019-00814-w)

2020

• Golyandina, N. and Zhigljavsky, A. 2020. Blind deconvolution of covariance matrix inverses for autoregressive processes. Linear Algebra and its Applications 593 , pp.188-211. (10.1016/j.laa.2020.02.005)
• Noonan, J. and Zhigljavsky, A. 2020. Power of the MOSUM test for online detection of a transient change in mean. Sequential Analysis 39 (2), pp.269-293. (10.1080/07474946.2020.1767406)
• Pepelyshev, A. and Zhigljavsky, A. 2020. Discrete uniform and binomial distributions with infinite support. Soft Computing 24 , pp.17517-17524. (10.1007/s00500-020-05190-2)
• Pronzato, L. and Zhigljavsky, A. 2020. Bayesian quadrature, energy minimization, and space-filling design. SIAM/ASA Journal on Uncertainty Quantification 8 (3), pp.959-1011. (10.1137/18M1210332)
• Zhigljavsky, A. and Noonan, J. 2020. Covering of high-dimensional cubes and quantization. SN Operations Research Forum 1 (3) 18. (10.1007/s43069-020-0015-8)

2019

• Dette, H. , Pepelyshev, A. and Zhigljavsky, A. 2019. The BLUE in continuous-time regression models with correlated errors. Annals of Statistics 47 (4), pp.1928-1959. (10.1214/18-AOS1734)
• Noonan, J. and Zhigljavsky, A. 2019. Approximating Shepp's constants for the Slepian process. Statistics and Probability Letters 153 , pp.21-31. (10.1016/j.spl.2019.05.001)
• Phillips, T. R. L. , Schmidt, K. M. and Zhigljavsky, A. 2019. Extension of the Schoenberg theorem to integrally conditionally positive definite functions. Journal of Mathematical Analysis and Applications 470 (1), pp.659-678. (10.1016/j.jmaa.2018.10.032)
• Pronzato, L. and Zhigljavsky, A. 2019. Measures minimizing regularized dispersion. Journal of Scientific Computing 78 (3), pp.1550-1570. (10.1007/s10915-018-0817-4)

2018

• Gillard, J. and Zhigljavsky, A. 2018. Optimal directional statistic for general regression. Statistics and Probability Letters 143 , pp.74. (10.1016/j.spl.2018.07.025)
• Gillard, J. and Zhigljavsky, A. 2018. Optimal estimation of direction in regression models with large number of parameters. Applied Mathematics and Computation 318 , pp.281-289. (10.1016/j.amc.2017.05.050)
• Noonan, J. and Zhigljavsky, A. 2018. Approximations of the boundary crossing probabilities for the maximum of moving weighted sums. Statistical Papers 59 (4), pp.1325-1337. (10.1007/s00362-018-1015-z)
• Pepelyshev, A. , Zhigljavsky, A. and Zilinskas, A. 2018. Performance of global random search algorithms for large dimensions. Journal of Global Optimization 71 , pp.57-71. (10.1007/s10898-017-0535-8)
• Pronzato, L. , Wynn, H. P. and Zhigljavsky, A. A. 2018. Simplicial variances, potentials and Mahalanobis distances. Journal of Multivariate Analysis 168 , pp.276-289. (10.1016/j.jmva.2018.08.002)

2017

• Dette, H. , Konstantinou, M. and Zhigljavsky, A. 2017. A new approach to optimal designs for correlated observations. Annals of Statistics 45 (4), pp.1579-1608. (10.1214/16-AOS1500)
• Pepelyshev, A. , Kornikov, V. and Zhigljavsky, A. 2017. Statistical estimation in global random search algorithms in case of large dimensions. Lecture Notes in Computer Science 10556 , pp.364-369. (10.1007/978-3-319-69404-7_32)
• Pepelyshev, A. and Zhigljavsky, A. 2017. SSA analysis and forecasting of records for Earth temperature and ice extents. Statistics and Its Interface 10 (1), pp.151-163. (10.4310/SII.2017.v10.n1.a14)
• Pronzato, L. , Wynn, H. P. and Zhigljavsky, A. 2017. Extended generalised variances, with applications. Bernoulli 23 (4A), pp.2617-2642. (10.3150/16-BEJ821)

2016

• Davies, G. , Gillard, J. and Zhigljavsky, A. 2016. Comparative study of different penalty functions and algorithms in survey calibration. In: Comparative Study of Different Penalty Functions and Algorithms in Survey Calibration. Vol. 107, , pp.87-127. (10.1007/978-3-319-29975-4_6)
• Dette, H. , Pepelyshev, A. and Zhigljavsky, A. 2016. Optimal designs for regression models with autoregressive errors. Statistics and Probability Letters 116 , pp.107-115. (10.1016/j.spl.2016.04.008)
• Dette, H. , Pepelyshev, A. and Zhigljavsky, A. 2016. Optimal designs in regression with correlated errors. Annals of Statistics 44 (1), pp.113-152. (10.1214/15-AOS1361)
• Gillard, J. W. and Zhigljavsky, A. A. 2016. Weighted norms in subspace-based methods for time series analysis. Numerical Linear Algebra with Applications 23 (5), pp.947-967. (10.1002/nla.2062)
• Gillard, J. W. and Zhigljavsky, A. 2016. Global optimization for structured low rank approximation. Presented at: International Conference of Numerical Analysis and Applied Mathematics 2015 Rhodes, Greece 22-28 September 2015. AIP Conference Proceedings. Vol. 1738.American Institute of Physics. , pp.400003. (10.1063/1.4952191)
• Pepelyshev, A. , Staroselskiy, Y. and Zhigljavsky, A. 2016. Adaptive targeting for online advertisement. Presented at: International Workshop on Machine Learning, Optimization and Big Data Taormina, Italy 21-23 July 2015. Published in: Pardalos, P. et al., Machine Learning, Optimization, and Big Data: First International Workshop, MOD 2015, Taormina, Sicily, Italy, July 21-23, 2015, Revised Selected Papers. Vol. 9432.Lecture Notes in Computer Science Springer Verlag. , pp.240-251. (10.1007/978-3-319-27926-8_21)
• Pepelyshev, A. et al. 2016. Adaptive targeting in online advertisement: models based on relative influence of factors. Presented at: International Workshop on Machine Learning, Optimization and Big Data Volterra, Italy 26-29 August 2016. Published in: Pardalos, P. et al., Machine Learning, Optimization, and Big Data. MOD 2016. Vol. 10122.Lecture Notes in Computer Science Springer. , pp.159-169. (10.1007/978-3-319-51469-7_13)
• Pepelyshev, A. , Staroselskiy, Y. and Zhigljavsky, A. A. 2016. Adaptive designs for optimizing online advertisement campaigns. Presented at: 11th International Workshop in Model-Oriented Design and Analysis Hamminkeln, Germany 12-17 June 2016. Published in: Kunert, J. , Muller, C. H. and Atkinson, A. C. eds. mODa 11 - Advances in Model-Oriented Design and Analysis: Proceedings of the 11th International Workshop in Model-Oriented Design and Analysis held in Hamminkeln, Germany, June 12-17, 2016. Contributions to Statistics Springer Verlag. , pp.199-208. (10.1007/978-3-319-31266-8_23)
• Pronzato, L. , Wynn, H. P. and Zhigljavsky, A. 2016. Extremal measures maximizing functionals based on simplicial volumes. Statistical Papers 57 , pp.1059-1075. (10.1007/s00362-016-0767-6)
• Z̆ilinskas, A. and Zhigljavsky, A. A. 2016. Branch and probability bound methods in multi-objective optimization. Optimization Letters 10 (2), pp.341-353. (10.1007/s11590-014-0777-z)

2015

• Davies, G. P. , Gillard, J. W. and Zhigljavsky, A. A. 2015. Calibration in survey sampling as an optimization problem. In: Migdalas, A. and Karakitsiou, A. eds. Optimization, Control, and Applications in the Information Age. Vol. 130, Springer Proceedings in Mathematics & Statistics Vol. 130.Springer. , pp.67-89. (10.1007/978-3-319-18567-5_4)
• Dette, H. , Pepelyshev, A. and Zhigljavsky, A. 2015. Design for linear regression models with correlated errors. In: Dean, A. et al., Handbook of Design and Analysis of Experiments. Chapman & Hall/CRC Handbooks of Modern Statistical Methods CRC Press. , pp.236-276.
• Gillard, J. W. and Zhigljavsky, A. A. 2015. Stochastic algorithms for solving structured low-rank approximation problems. Communications in Nonlinear Science and Numerical Simulation 21 (1-3), pp.70-88. (10.1016/j.cnsns.2014.08.023)

2014

• Dette, H. , Pepelyshev, A. and Zhigljavsky, A. 2014. ‘Nearly’ universally optimal designs for models with correlated observations. Computational Statistics & Data Analysis 71 , pp.1103-1112. (10.1016/j.csda.2013.02.002)
• Pronzato, L. and Zhigljavsky, A. A. 2014. Algorithmic construction of optimal designs on compact sets for concave and differentiable criteria. Journal of Statistical Planning and Inference 154 , pp.141-155. (10.1016/j.jspi.2014.04.005)

2013

• Dette, H. , Pepelyshev, A. and Zhigljavsky, A. A. 2013. Optimal design for linear models with correlated observations. Annals of Statistics 41 (1), pp.143-176. (10.1214/12-AOS1079)
• Gillard, J. W. and Zhigljavsky, A. A. 2013. Optimization challlenges in the structured low rank approximation problem. Journal of Global Optimization 57 (3), pp.733-751. (10.1007/s10898-012-9962-8)
• Hassani, H. , Heravi, S. and Zhigljavsky, A. A. 2013. Forecasting UK industrial production with multivariate singular spectrum analysis. Journal of Forecasting 32 (5), pp.395-408. (10.1002/for.2244)
• Schmidt, K. M. and Zhigljavsky, A. A. 2013. An extremal property of the generalized arcsine distribution. Metrika 76 (3), pp.347-355. (10.1007/s00184-012-0391-y)
• Zhigljavsky, A. , Pronzato, L. and Bukina, E. 2013. An asymptotically optimal gradient algorithm for quadratic optimization with low computational cost. Optimization Letters 7 (6), pp.1047-1059. (10.1007/s11590-012-0491-7)

2012

• Pronzato, L. , Zhigljavsky, A. and Bukina, A. 2012. Estimation of spectral bounds in gradient algorithms. Acta Applicandae Mathematicae 127 (1), pp.117-136. (10.1007/s10440-012-9794-z)

2011

• Gillard, J. W. and Zhigljavsky, A. A. 2011. Analysis of structured low rank approximation as an optimization problem. Informatica 22 (4), pp.489-505.
• Hassani, H. , Xu, Z. and Zhigljavsky, A. A. 2011. Singular spectrum analysis based on the perturbation theory. Nonlinear Analysis: Real World Applications 12 (5), pp.2752-2766. (10.1016/j.nonrwa.2011.03.020)
• Patterson, K. et al., 2011. Multivariate singular spectrum analysis for forecasting revisions to real-time data. Journal of Applied Statistics 38 (10), pp.2183-2211. (10.1080/02664763.2010.545371)
• Pronzato, L. and Zhigljavsky, A. A. 2011. Gradient algorithms for quadratic optimization with fast convergence rates. Computational Optimization and Applications 50 (3), pp.597-617. (10.1007/s10589-010-9319-5)
• Zhigljavsky, A. A. 2011. Statistical Modelling in Market Research. In: Lovric, M. ed. International Encyclopedia of Statistical Science. Springer Reference Berlin: Springer. , pp.1450-1452. (10.1007/978-3-642-04898-2_548)

2010

• Hassani, H. , Soofi, A. and Zhigljavsky, A. A. 2010. Predicting daily exchange rate with singular spectrum analysis. Nonlinear Analysis: Real World Applications 11 (3), pp.2023-2034. (10.1016/j.nonrwa.2009.05.008)
• Pepelyshev, A. and Zhigljavsky, A. A. 2010. Assessing the stability of long-horizon SSA forecasting. Statistics and Its Interface 3 (3), pp.321-327.
• Zhigljavsky, A. A. 2010. Nonadaptive group testing with lies: Probabilistic existence theorems. Journal of Statistical Planning and Inference 140 (10), pp.2825-2893. (10.1016/j.jspi.2010.03.012)
• Zhigljavsky, A. A. 2010. Singular Spectrum Analysis for time series: Introduction to this special issue. Statistics and Its Interface 3 (3), pp.255-258.
• Zhigljavsky, A. A. , Dette, H. and Pepelyshev, A. 2010. A new approach to optimal design for linear models with correlated observations. Journal of the American Statistical Association 105 (491), pp.1093-1103. (10.1198/jasa.2010.tm09467)
• Zhigljavsky, A. A. and Hamilton, E. 2010. Stopping rules in k-adaptive global random search algorithms. Journal of Global Optimization 48 (1), pp.87-97. (10.1007/s10898-010-9528-6)

2009

• Dette, H. et al., 2009. Asymptotic optimal designs under long-range dependence error structure. Bernoulli 15 (4), pp.1036-1056. (10.3150/09-BEJ185)
• Hassani, H. , Heravi, S. and Zhigljavsky, A. A. 2009. Forecasting European industrial production with singular spectrum analysis. International Journal of Forecasting 25 (1), pp.103-118. (10.1016/j.ijforecast.2008.09.007)
• Hassani, H. and Zhigljavsky, A. A. 2009. Singular spectrum analysis: methodology and application to economics data. Journal of Systems Science and Complexity 22 (3), pp.372-394. (10.1007/s11424-009-9171-9)
• Schmidt, K. M. and Zhigljavsky, A. A. 2009. A characterization of the arcsine distribution. Statistics & Probability Letters 79 (24), pp.2451-2455. (10.1016/j.spl.2009.08.018)

2008

• Dette, H. , Pepelyshev, A. and Zhigljavsky, A. A. 2008. Improving updating rules in multiplicative algorithms for computing D-optimal designs. Computational Statistics & Data Analysis 53 (2), pp.312-320. (10.1016/j.csda.2008.10.002)

2007

• Fedorov, V. et al., 2007. Deriving approximations in a random effects model for multicentre clinical trials with binary response. Communications in Statistics - Theory and Methods 36 (3), pp.629-644. (10.1080/03610920601001832)
• Leonenko, N. N. , Savani, V. and Zhigljavsky, A. A. 2007. Autoregressive negative binomial processes. Annales de l'Institut de Statistique de l'Universite de Paris 51 (1), pp.25-47.
• Savani, V. and Zhigljavsky, A. A. 2007. Asymptotic distributions of statistics and parameter estimates for mixed Poisson processes. Journal of Statistical Planning and Inference 137 (12), pp.3990-4002. (10.1016/j.jspi.2007.04.016)

2006

• Pronzato, L. , Wynn, H. P. and Zhigljavsky, A. A. 2006. Asymptotic behaviour of a family of gradient algorithms in Rd and Hilbert spaces. Mathematical Programming 107 (3), pp.409-438. (10.1007/s10107-005-0602-7)
• Savani, V. and Zhigljavsky, A. A. 2006. Efficient Estimation of Parameters of the Negative Binomial Distribution. Communications in Statistics - Theory and Methods 35 (5), pp.767-783. (10.1080/03610920500501346)
• Savani, V. and Zhigljavsky, A. A. 2006. Efficient parameter estimation for independent and INAR(1) negative binomial samples. Metrika 65 (2), pp.207-225. (10.1007/s00184-006-0071-x)

2004

• Moshchevitin, N. and Zhigljavsky, A. A. 2004. Entropies of the partitions of the unit interval generated by the Farey tree. Acta Arithmetica 115 (1), pp.47-58.

2003

• Zhigljavsky, A. A. 2003. Probabilistic existence theorems in group testing. Journal of Statistical Planning and Inference 115 (1), pp.1-43. (10.1016/S0378-3758(02)00148-9)

2001

• Golyandina, N. , Nekrutkin, V. V. and Zhigljavsky, A. A. 2001. Analysis of time series structure: SSA and related techniques. Monographs on Statistics & Applied Probability Chapman & Hall/ CRC.

1999

• Aliev, I. and Zhigljavsky, A. 1999. Weyl sequences: asymptotic distributions of the partition lengths. Acta Arithmetica 88 (4), pp.351-361.