Publications 

MONOGRAPHS

 

Stochastic global optimization:

  • Zhigljavsky A.A., Zilinskas A.G. (2008) Stochastic Global Optimization, Springer-Verlag, Berlin et al., xvi+362 pp.
  • Zhigljavsky A.A. (1991) Theory of Global Random Search. Kluwer Academic Press, Dordrecht e.a. xviii+342 pp.
  • Zhigljavsky A.A., Zilinskas A.G. (1991) Search for Global Extremum. Nauka, Moscow, 248 pp. (in Russian).
  • Zhigljavsky A.A.(1985) Mathematical Theory of the Global Random Search. St.Petersburg University Press, 296 pp. (in Russian).

  

 Time series analysis:

  • Golyandina N.E., Zhigljavsky A.A. (2013) Singular Spectrum Analysis for Time Series, Springer-Verlag, Berlin et al., vii+120pp. 
  • Golyandina N.E., Nekrutkin V.V., Zhigljavsky A.A. (2001) Analysis of Time Series Structure: SSA and related technique, Chapman & Hall / CRS, Boca Raton, xii+306pp. 
  • Zhigljavsky A.A., Kraskovsky A.E. (1988) Detection of Abrupt Changes of Random Processes in Radiotechnics Problems. St.Petersburg University Press, 222 pp. (in Russian).

  

Optimal experimental design:

  • Ermakov S.M., Zhigljavsky A.A. (1987) Mathematical Theory of Optimal Experiment. Nauka, Moscow, 320 pp. (in Russian).

     

Dynamical systems in search and optimization:

  • Pronzato L., Wynn H.P., Zhigljavsky A.A. (2000) Dynamical Search: Application of Dynamical Systems in Search and Optimization, Chapman & Hall / CRS, Boca Raton, xvi + 222pp.

 

                               EDITED VOLUMES

  • Wang S., Zhang H., Zhigljavsky A., eds (2017) Statistics and Its Interface, Special issue on Time Series Analysis and Applications in Economics and Climate (vol.10, No.1)  
  • Pardalos P., Zilinskas J., Zhigljavsky A., eds (2016) Advances in Stochastic and Deterministic Global Optimization, Springer-Verlag, Berlin et al., xvi+316 pp.
  • Brugnano L.,Sergeyev Ya.., Zhigljavsky A., eds. (2015) Communications in Nonlinear Science and Numerical Simulation (vol. 21, No. 1-3), Special issue on Numerical Computations: Theory and Algorithms. 
  • Sergeyev Ya., De Leone R., Zhigljavsky A., eds. (2012) Applied Mathematics and Computation (vol. 218, No. 16), Special issue on Infinite and Infinitesimal in Mathematics, Computing and Natural Sciences. 
  • Zhigljavsky A.A., guest editor (2010), Statistics and Its Interface (vol. 3, No. 3), Special issue on the Singular Spectrum Analysis in Time Series. 
  • Pronzato L. and Zhigljavsky A.A., eds. (2008) In search for optimality in optimization and statistics, Springer-Verlag, 224 pp.
  • Atkinson A.C., Bogacka B., Zhigljavsky A.A., eds. (2001) Optimum Design - 2000, Kluwer Academic Publishers, x+306 pp.
  • Nekrutkin V.V., Zhigljavsky A.A., eds. (1999) Statistical Analysis in Clinical Studies. University of St.Petersburg, 342 pp. (in Russian) 
  • Danilov D., Zhigljavsky A.A., eds. (1997) Principal Components of Time Series:
    The Caterpillar Method. University of St.Petersburg, 308 pp. (in Russian) 
  • Zhigljavsky A.A., ed. (1995) Oral Care Statistical Studies, University of St.Petersburg, x+205 pp.
  • Muller W., Wynn H.P., Zhigljavsky A.A., eds. (1993) Model Oriented Data Analysis, Physica-Verlag, Berlin, xiii+287 pp.
  • Zhigljavsky A.A., guest editor (1993) Acta Applicandae Mathematicae, 33, No. 1.

SELECTED PAPERS

Optimal experimental design:

  • Pronzato L., Wynn H.P., Zhigljavsky A.A. (2005) Kantorovich-type inequalities for operators via D-optimal design theory.  Linear Algebra Appl., 410, 160--169.pdf
  • Dette H., Pepelyshev A.,  Zhigljavsky, A. (2008) Improving Updating Rules in Multiplicative Algorithms for Computing D-Optimal Designs, Computational Statistics and Data Analysis, v. 53, No. 2, p. 312-320.pdf
  • Dette H., Leonenko N., Pepelyshev A., Zhigljavsky, A. (2009) Asymptotic optimal designs under long-range dependence error structure, Bernoulli, v. 15, p. 1036-1056.pdf
  • Zhigljavsky A., Dette H. and Pepelyshev A. (2010).  A new approach to optimal design for linear models with correlated observations, J. of American Statist. Assoc., v. 105, No. 491, 1093-1103.pdf
  • Dette H.,Pepelyshev A., Zhigljavsky A. (2013) ‘Nearly’ universally optimal designs for models with correlated observations, Computational Statistics & Data Analysis, 71 (C), 1103-1112.
  • Dette H.,Pepelyshev A., Zhigljavsky A. (2013) Optimal design for linear models with correlated observations, The Annals of Statistics, v. 41, No. 1, 143-176.
  • Pronzato L., & Zhigljavsky A. (2014). Algorithmic construction of optimal designs on compact sets for concave and differentiable criteria. Journal of Statistical Planning and Inference, 154, 141-155.
  • Dette H.,Pepelyshev A., Zhigljavsky A. (2015) Design for Linear Regression Models with Correlated Errors. Handbook of Design and Analysis of Experiments, 7, pp. 237—276.
  • Dette, H., Pepelyshev, A., & Zhigljavsky, A. (2016). Optimal designs in regression with correlated errors, The Annals of Statistics. V. 44, No. 1, pp.113-152
  • Dette, H., Konstantinou M., & Zhigljavsky, A. (2016) A new approach to optimal designs for correlated observations, The Annals of Statistics (to appear)

 

Applied statistics and probability:

  • Jones C.M. and Zhigljavsky A.A. (2001) Comparison of costs for multi-stage group testing methods in the pharmaceutical industry, Communication in Statistics - Theory and Methods, 30, 2189-2209.pdf
  • Bond B., Fedorov V.V., Jones C.M., and  Zhigljavsky A.A.(2001) Pharmaceutical applications of the multi-stage group testing, in: Optimum Design - 2000 (Atkinson A.C., Bogacka B., Zhigljavsky A.A., eds.),  Kluwer Academic Publishers, 155-166. pdf
  • Sahu S.K., Zhigljavsky A.A. (2003) Self-regenerative Markov Chain Monte Carlo with adaptation, Bernoulli, v. 9, No. 3, 395-422.pdf
  • Jones C.M. and Zhigljavsky A.A. (2004) Approximating the negative moments of the Poisson distribution. Statistics and Probability Letters, v. 66, 171-181. pdf
  • Fedorov, V.,  Jones, B.,  Jones, C. M.,  Zhigljavsky, A. (2004) Estimation of the treatment difference in multicenter trials. J. Biopharm. Statist.  14,  no. 4, 1037-1063.pdf
  • Fedorov, V.,  Jones, B.,  Jones, C. M.,  Zhigljavsky, A. (2005) Multi-center clinical trials with random enrollment: theoretical approximations. Comm. Statist. Theory Methods  34,  no. 4, 955--985.pdf
  • Savani, V. ,  Zhigljavsky, A.A. (2006) Efficient estimation of parameters of the negative binomial distribution. Comm. Statist.: Theory and Methods  35,  No. 4-6, 767--783.pdf
  • Savani, V. ,  Zhigljavsky, A.A. (2007) Efficient parameter estimation for independent and INAR(1) negative binomial samples. Metrika, v. 65, no. 2, 207-225.pdf
  • Fedorov, V.,  Jones, B.,  Savani V. , Zhigljavsky, A. (2007) Deriving approximations in a random effects model for multicentre clinical trials with binary response. Communications in Statistics: Theory and Methods, v. 37. No. 3, 629-644.pdf
  • Leonenko N., Savani, V. ,  Zhigljavsky, A.A. (2007) Autoregressive negative binomial processes, Annales de l’I.S.U.P, v. LI, No. 1-2, 25-47. pdf
  • Savani V., and Zhigljavsky A. (2007) Asymptotic distributions of statistics and parameter estimates for mixed Poisson processes, Journal of Statistical Planning and Inference, v. 137, No. 12, 3990-4002. pdf
  • Schmidt K.-M., Zhigljavsky, A. (2009) A Characterization of the arcsine distribution, Statistics and Probability Letters, v. 79, p. 2451-2455.pdf
  • Zhigljavsky A. (2011) Statistical Modelling in Market Research.  In: International Encyclopedia of Statistical Science, Springer, 1450-1452.pdf
  • Phillips T. R. L., Zhigljavsky A. (2014) Approximation of inverse moments of discrete distributions. Statistics & Probability Letters, 94, 135-143.
  • Pronzato, L., Wynn, H., & Zhigljavsky, A. (2016). An extended Generalised Variance, with Applications. Bernoulli (to appear).
  • Pronzato, L., Wynn, H., & Zhigljavsky, A. (2016). Extremal measures maximizing functionals based on simplicial volumes, Statistical Papers (to appear).
  • Pepelyshev A., Staroselskiy Y. and Anatoly Zhigljavsky A. (2015) Adaptive Targeting for Online Advertisement," Machine Learning, Optimization, and Big Data. Springer International Publishing, 2015. Lecture Notes in Computer Science, Vol. 9432, pp. 240-251.
  • Zhigljavsky, A., Golyandina N. and Gryaznov S. (2016) Deconvolution of a discrete uniform distribution, Statistical and Probability Letters, vol. 118, pp. 37-44.

 

Stochastic global optimization:

  • Kondratovich M.,  Zhigljavsky A. (1998) Comparison of independent and stratified sampling schemes in problems of global optimization.  Monte Carlo and Quasi-Monte Carlo Methods (H. Niederrreiter, P. Hellekalek, G. Larcher, P. Zinterhof, eds). Lecture notes in statistics, v. 127, pp. 292-299. pdf
  • Hamilton, E., Savani, V.,  Zhigljavsky, A. (2007) Estimating the minimal value of a function in global random search: comparison of estimation procedures. In: Models and algorithms for global optimization, Springer Optimization and its Applications, vol. 4, Springer, New York, p. 193—214.pdf
  • Zhigljavsky A, Hamilton E. (2010) Stopping rules in k-adaptive global random search algorithms. Journal of Global Optimization, v. 48, No. 1, 87–97. pdf
  • Zhigljavsky, A (2011) Stochastic Global Optimization.  In: International Encyclopedia of Statistical Science, Springer,1521-1524.pdf
  • Zilinskas A. and Zhigljavsky, A. (2016). Branch and probability bound methods in multi-objective optimization, Optimization Letters, Vol. 10, No. 2, pp. 341-353
  • Zilinskas A. and Zhigljavsky, A. (2016). Stochastic Global Optimization: A Review on the Occasion of 25 Years of Informatica. Informatica, 2016, Vol. 27, No. 2, 229-256.

 

Singular Spectrum analysis for time series:

  • Moskvina V.G. and Zhigljavsky A.A. (2003) An algorithm based on singular spectrum analysis for change-point detection, Communication in Statistics - Simulation and Computation, v. 32, No. 2, 319-352. pdf
  • Hassani H. and Zhigljavsky A.(2009) Singular Spectrum Analysis: Methodology and Application to Economics Data, Journal of Systems Science and Complexity, v. 22, No. 3, p. 372-394.pdf
  • Hassani H., Heravi S. and Zhigljavsky A. (2009) Forecasting European Industrial Production with Singular Spectrum Analysis, International Journal of Forecasting,  25, No. 1, p. 103-118.pdf
  • Hassani H., Soofi A. and Zhigljavsky A. (2010) Predicting Daily Exchange Rate with Singular Spectrum Analysis Data, Nonlinear Analysis: Real World Applications, v. 11  No. 3, 2023—2034.pdf
  • Zhigljavsky A. (2010).  Singular spectrum analysis for time series: introduction. Statistics and Its Interface, v. 3, No. 3, 255--258.pdf
  • Zhigljavsky A. (2011) Singular Spectrum Analysis for Time Series. In: International Encyclopedia of Statistical Science, Springer,1335-1337.pdf
  • Pepelyshev A. and  Zhigljavsky A. (2010)  Assessing the stability of long-horizon SSA forecasting. Statistics and Its Interface, v.  3  No. 3, 321--327pdf
  • Rodríguez-Aragón L.J. and  Zhigljavsky A. (2010).  Singular spectrum analysis for image processing. Statistics and Its Interface, v. 3, No. 3, 419--426.pdf
  • Hassani, H; Zhigljavsky, A; Patterson, K; Soofi, A. (2011). A Comprehensive Causality Test Based on the Singular Spectrum Analysis, Causality in Science (eds. P. M. Illari, F. Russo and J. Williamson), Oxford University press, 379-404.pdf
  • Hassani H., Z. Hu  and and Zhigljavsky A. (2011)  Singular spectrum analysis based on the perturbation theory, Nonlinear Analysis: Real World Applications, v. 12  No. 5, 2752-2766.pdf
  • Patterson K., Hassani H., Heravi S. and Zhigljavsky A. (2011) Multivariate singular spectrum analysis for forecasting revisions to real-time data, Journal of Applied Statistics, v. 38, No. 10, 2183-2211 pdf

 

Dynamical systems in search and optimization:

  • Pronzato L., Wynn H.P., Zhigljavsky A.A. (1997) Stochastic analysis of convergence via dynamic representation for a class of line-search algorithms. Combinatorics, Probability and Computing, 6, 205-229.pdf
  • Pronzato L., Wynn H.P., Zhigljavsky A.A. (1998) A generalised Golden-Section algorithm for line--search, IMA Journal on Math. Control and Information, 15, 185-214. pdf
  • Pronzato L., Wynn H.P., Zhigljavsky A.A. (1999) Finite sample behaviour of an ergodically fast line-search algorithm, Computational Optimisation and Applications, 14, 75-86.pdf
  • Pronzato L., Wynn H.P., Zhigljavsky A.A. (2001) Analysis of performance of symmetric second-order line search algorithms through continued fractions,  IMA J of Math Control and Information, 18, 281-296.pdf
  • Pronzato L., Wynn H.P., Zhigljavsky A.A. (2001) Renormalised steepest descent in Hilbert space converges to a two-point attractor, Acta Applicandae Mathematicae, 67, 1-18.pdf
  • Pronzato L., Wynn H.P., Zhigljavsky A.A. (2002) An introduction to dynamical search, in: Handbook of Global Optimization, Vol. 2, Kluwer Academic Publishers, Dordrecht, pp. 115-150.  pdf
  • Pronzato L., Wynn H.P., Zhigljavsky A.A. (2006) Asymptotic behaviour of a family of gradient algorithms in R^d and Hilbert spaces.  Math. Program. 107, No. 3, Ser. A, 409--438.pdf
  • Haycroft R., Pronzato L., Wynn H.P., Zhigljavsky A.A. (2008) Studying Convergence of Gradient Algorithms via Optimal Experimental Design Theory, In: Search for optimality in design and statistics, Springer-Verlag, p. 13-37.pdf
  • Pronzato L., Wynn H.P., Zhigljavsky A.A. (2008) A dynamical-system analysis of the optimum s-gradient algorithm, In: Search for optimality in design and statistics, Springer-Verlag, p. 39-80.pdf
  • Pronzato L. and Zhigljavsky A. (2010) Gradient algorithms for quadratic optimization with fast convergence rates, Computational Optimization and Applications, v. 45, No. 1, 35-49. DOI 10.1007/s10589-010-9319-5 pdf
  • Pronzato L., Zhigljavsky A., Bukina E. (2013) Estimation of spectral bounds in gradient algorithms, Acta Applicandae Mathematicae, v. 127, No. 1, 117-136.

 

Probabilistic methods in discrete search:

  • O’Geran J.,Wynn, H.P., Zhigljavsky, A. (1993) Mastermind as a test-bed for search algorithms. Chance 6,  no. 1, 31--37.pdf
  • Wynn, H.P., Zhigljavsky, A. (1994) The theory of search from a statistical viewpoint. With discussion and a reply by the authors. Test 3,  no. 2, 1--45.pdf
  • Zhigljavsky A., Zabalkanskaya L. (1996) Existence theorems for some group testing strategies,  Journal of Statistical Planning and Inference, 55, 151—173.pdf
  • Zhigljavsky A. (2003) Probabilistic existence theorems in group testing, Journal of Statistical Planning and Inference, v. 115, No. 1, 1 - 43.pdf
  • Zhigljavsky A. (2010) Nonadaptive group testing with lies: Probabilistic existence theorems. Journal of Statistical Planning and Inference, v. 140, No. 10, 2825 – 2893.pdf

 

Probabilistic number theory:

  • Kargaev P.P., Zhigljavsky A.A. (1996) Approximation of real numbers by rationals: some metric theorems, Journal of Number Theory, 61, 209--225.pdf
  • Kargaev P., Zhigljavsky  A. (1997) Asymptotic distribution of the distance function to the Farey points, Journal of Number Theory, 65, 130-149.pdf
  • Zhigljavsky A.A., Aliev I. (1999) Weyl sequences: asymptotic distributions of the partition lengths, Acta Arithmetica, LXXXVIII.4, 351-361.pdf
  • Huxley M.N. and Zhigljavsky A.A. (2001) On the distribution of Farey fractions and hyperbolic lattice points, Periodica Matematica Hungarica, 42, 191-198.pdf
  • Moshchevitin N. and Zhigljavsky A.A. (2004) Entropies of the partitions of the unit interval generated by the Farey tree, Acta Arithmetica, vol. 115, 47-58.pdf

 

Low-rank approximation of structured matrices:

  • Gillard J., Zhigljavsky A. (2011) Analysis of structured low rank approximation as an optimization problem. Informatica, v. 22, No. 4, 489-505.
  • Gillard J., Zhigljavsky A. (2013). Optimization challenges in the structured low rank approximation problem. Journal of Global Optimization, 1-19.
  • Gillard J., Zhigljavsky A. (2015) Stochastic algorithms for solving structured low-rank matrix approximation problems, Communications in Nonlinear Science and Numerical Simulation, v. 21, No. 1, 70-88
  • Gillard J., Zhigljavsky A. (2015). Application of structured low-rank approximation methods for imputing missing values in time series. Statistics and Its Interface, v. 8, No. 3, 321-330.
  • Gillard J. and Zhigljavsky, A. (2016) Weighted norms in subspace-based methods for time series analysis, Numerical Linear Algebra with Applications (to appear)

 

 

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