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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.,
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
- Zhigljavsky A.A.,
guest editor (2010) Statistics and Its Interface, special issue devoted
to the Singular Spectrum Analysis for time series (in preparation)
- 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
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
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 (accepted, published on-line).pdf
- Zhigljavsky, A
(2011) Stochastic Global Optimization. In: International Encyclopedia of
Statistical Science, Springer,1521-1524.pdf
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
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
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 (to appear), DOI 10.1007/s10589-010-9319-5
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
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