01.01.09 (Discrete mathematics and mathematical cybernetics)
Birth date:
19.10.1952
E-mail:
Keywords:
mathematical statistics; minimax procedures; game theory; 2-person games; decision theory, game-theory methods for estimation of knowledge level.
Subject:
The game theoretic approach to setting and solution of statistical problems is found for confidence interval estimation problem of parameter of the binomial and Hyper geometric distributions. The confidence probability and the minimax decision function are constructed for any set of admissible intervals. One half of the consructed confidence intervals is shorter than classical CIs for the same confidence probabilities. The minimax decision function under consideration enables observation number to be reduced by about 1.5 times from the classical approach for the same reliability and accuracy.
Biography
Graduated from Faculty of Mechanics and Mathematics of Leningrad State University (LSU) in 1974 (department of operation research). Ph.D. thesis was defended in 1980. D.Sci.thesis was defended in 1992. Professor of Mathematics department from 1994.
Member of Internationa Academia of Universities supervisor of grants of RFBR in 1998–1999, 2000–2002.
Main publications:
Lutsenko M. M., Maloshevskii S. G. Minimax confidence intervals for the binomial parameter // J. Statist. Plann. Inference, 2003, 113(1), 67–77.
Lutsenko M. M. Statistical games for discrete distributions // Lecture Notes in Econom. and Math. Systems, 2002, 510, 533–548.
Lutsenko M. M., Ivanov M. A. Minimax confidence intervals for the parameter of hypergeometric distribution // Automat. Remote Control, 2000, 61(7), Part 1, 1125–1132.
Lutsenko M. M. Game of timing with additional discontinuity lines // Intern. Conference "Logic, Game Theory and Social Choice". St.Petersburg, 2001, 158–163.
Lutsenko M. M. A game-theoretic method for the estimation of a parameter of the binomial law //Theoret. Probab. Appl., 1990, 35, 467–477.
Mikhail M. Lutsenko, “Generalized integral equations for timing games”, Contributions to Game Theory and Management, 16 (2023), 182–191
2017
2.
M. M. Lutsenko, N. V. Shadrinceva, “Shapley weights of test items”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 13:3 (2017), 300–312
Mikhail M. Lutsenko, Natalia V. Shadrintseva, “Cooperative method for assignment of item weights in educational test”, Mat. Teor. Igr Pril., 6:4 (2014), 37–67
M. A. Ivanov, M. M. Lutsenko, “Minimax confidence intervals for the parameter of a hypergeometric distribution”, Avtomat. i Telemekh., 2000, no. 7, 68–76; Autom. Remote Control, 61:7 (2000), 1125–1132
M. M. Lutsenko, “A game-theoretic method for estimating the parameter of a binomial law”, Teor. Veroyatnost. i Primenen., 35:3 (1990), 471–481; Theory Probab. Appl., 35:3 (1990), 467–477
M. M. Lutzenko, “A Theoretic-Game Method of the Estimation of the Parameter of a Binomial Law Based on a Single Observation”, Teor. Veroyatnost. i Primenen., 34:3 (1989), 589–593; Theory Probab. Appl., 34:3 (1989), 531–535
M. M. Lucenko, “The problem of $\delta$-meeting on a $3$-dimensional ball”, Teor. Veroyatnost. i Primenen., 23:1 (1978), 198–203; Theory Probab. Appl., 23:1 (1978), 190–195
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