Zakład Statystyki Matematycznej

Kierownik:

Pracownicy:

O Zakładzie

The Section of Mathematical Statistics was established on April 1, 2004, as a unification of Section of Mathematical Statistics and Its Applications and Section of Applied Probability. For brief history of the two last mentioned Sections see below.

The following researchers have been members of the Section of Mathematical Statistics: Tadeusz Bednarski, Przemysław Biecek, Katarzyna Danielak, Tadeusz Inglot, Teresa Ledwina, Ryszarda Rempała, Tomasz Rychlik and Ryszard Zieliński. The main scientific interests have been focused on the following topics:

  • asymptotic optimality and efficiency of tests,
  • characterizations by means of ordered statistical data,
  • data driven tests,
  • general methodology for robust estimation and testing,
  • methods of model selection,
  • multiple testing procedures,
  • optimal bounds on statistical functionals,
  • optimal nonparametric quantile estimation,
  • sequential decision problems for controlling production, distribution and inventory processes.

Selected publications:

  • T. Bednarski (2004). Robust estimation in the generalized Poisson model, Statistics 38, 149-159.
  • M. Bogdan, F. Frommlet, P. Biecek, R. Cheng, J.K. Ghosh, R.W. Doerge (2008). Extending the modified Bayesian Information Criterion (mBIC) to dense markers and multiple interval mapping, Biometrics 64, in press.
  • K. Danielak (2005). Distribution-free bounds for expectations of increments of records, J. Statist. Plann. Inf. 133, 239-247.
  • T. Inglot, T. Ledwina (2004). On consistent minimax distinguishability and intermediate efficiency of Cramér-von Mises test, J. Statist. Plann. Inf. 124, 453-474.
  • T. Inglot, T. Ledwina (2006). Data driven score tests for a homoscedastic linear regression model: asymptotic results, Probab. Math. Statist. 26, 41-61.
  • J. Navarro, T. Rychlik (2007). Reliability and expectation bounds for coherent systems with exchangeable components, J. Multivar. Anal. 98, 102-113.
  • W. Niemiro, R. Zieliński (2007). Uniform asymptotic normality for the Bernoulli scheme, Appl. Math. 34, 215-221.

Seminars:

  • Asymptotic Statistics (T. Inglot, T. Ledwina; Wrocław),
  • Mathematical Statistics and other Probabilistic Applications (M. Męczarski, J. Mielniczuk, T. Rychlik; Warszawa),
  • Statistics in Medicine (P. Biecek; Wrocław).


The Section of Mathematical Statistics and Its Applications

The Section of Mathematical Statistics and Its Applications stemmed from the Department of Applied Mathematics of the State Institute of Mathematics, which was established November 20, 1948. In 1950 the Department was split into two sections: the Section of Statistical Quality Control, founded in Warsaw, and the Section of Applications to Biology, Economics and Technology, which was located in Wrocław.

Wrocław's section was directed by Hugo Steinhaus until his retirement in 1960. Julian Perkal (1960-1965) and Stefan Zubrzycki (1965-1968) were later directors. The Section has played a very important role in the Wrocław scientific community, in particular through many collaborations with various professionals and educational work in applied probability and statistics. The Zastosowania Matematyki (Applicationes Mathematicae) journal, founded by Hugo Steinhaus, in 1953 with help of Jan Oderfeld, was a significant platform for the activity of the group. This activity was further supported by Julian Perkal, who founded the Listy Biometryczne journal in 1964.

From 1968 to 1991 the Section was headed by Witold Klonecki and was renamed the Section of Mathematical Statistics and Its Applications in 1973. At that time, the main activity was focused on PhD studies in modern statistical methodology, initially with the kind aid of colleagues from Wrocław University. Members of the group participated very actively in the organization of a series of conferences, beginning with one in Wisła in 1973. Many of these conferences were international. The European Meeting of Statisticians (1981) and Banach Center Semester on Nonparametric and Robust Methods (1984) are prominent examples. Witold Klonecki was also one of the founders of the Probability and Mathematical Statistics journal (1980).

Since 1991 until 2004 the Section was headed by Tadeusz Bednarski. Apart from research in mathematical statistics, much attention was focused on direct applied work. This was achieved by cooperation with research groups in the Medical Academy, Technical University and Agricultural University of Wrocław.

Selected publications:

  • K. Florek, J. Łukaszewicz, J. Perkal, H. Steinhaus, S. Zubrzycki (1952). Sur la liaison et la division des points d'un ensemble fini, Colloq. Math. 2, 282-285.
  • H. Steinhaus (1954). On establishing paternity [in Polish], Zastosow. Mat. I, 67-82.
  • J. Perkal (1956). On the $epsilon$-length, Bull. Acad. Pol. Sci. 4, 399-403.
  • H. Steinhaus (1957). The problem of estimation, Ann. Math. Statist. 28, 633-648.
  • S. Zubrzycki (1957). On estimating gangue parameters, Zastosow. Mat. III, 105-153.
  • E. Marczewski, H. Steinhaus (1959). On the systematic distance of biotopes, [in Polish], Zastosow. Mat. 4, 195-203.
  • H. Steinhaus, K. Urbanik (1959). Poissonsche Folgen (Leon Lichtenstein zum Gedächtnis), Math. Zeitsch. 72, 127-145.
  • H. Steinhaus (1960). Definitions for a theory of games and pursuits, Naval Research Logistic Quaterly 7, 105-108.
  • T. Dalenius, J. Hájek, S. Zubrzycki (1961). On plane sampling and related geometrical problems, in : Proc. Fourth Berkeley Symp. Math. Statist. Probab. 1, 125-130.
  • J. Perkal (1962). A design for a genetic test [in Polish], Zastosow. Mat. VI, 257-285.
  • S. Zubrzycki (1966). Explicit formulas for minimax admissible estimators in some cases of restrictions imposed on the parameter, Zastosow. Mat. 9, 31-52.
  • A. S. Kozek (1977). Efficiency and Cramér-Rao type inequalities for convex loss functions, J. Multivariate Anal. 7, 89-106.
  • M. Musiela (1977). Sequential estimation of parameters of a stochastic differential equation, Math. Operationsforsch. Statist. Ser. Statist. 8, 483-498.
  • T. Ledwina (1978). Admissible tests for exponential families with finite support, Math. Operationsforsch. Statist. Ser. Statist. 9, 105-118.
  • R. Zmyślony (1980). A characterization of best unbiased estimators in the general linear model, in : Mathematical Statistics and Probability Theory (Proc. Sixth International Conf. Wisła 1978), Lecture Notes in Statist. 2, Springer-Verlag, 365-378.
  • T. Bednarski (1981). On solutions of minimax test problems for special capacities, Z. Wahrsch. Verw. Gebiete 58, 397-405.
  • T. Bednarski (1982). Binary experiments, minimax tests and 2-alternating capacities, Ann. Statist. 10, 226-232.
  • T. Bednarski, S. Gnot, T. Ledwina (1982). Testing approximate validity of Hardy-Weinberg law in population genetics, in: Probability and Statistical Inference, Reidel, 35-46.
  • A.S. Kozek (1982). Towards a calculus for admisibility, Ann. Statist. 10, 825-837.
  • J. Zabrzeski, R. Zmyślony (1987). Experimental description of the rate of platinum and rodium losses in the process of ammonia oxidation, Appl. Catalisis 35, 13-22.
  • R.H. Farrel, W. Klonecki, S. Zontek (1989). All admissible linear estimators of the vector of gamma scale parameters with application to random effects models, Ann. Statist. 17, 268-281.
  • W. Klonecki, S. Zontek (1992). Admissible estimators of variance components obtained via submodels, Ann. Statist. 20, 1454-1467.
  • T. Bednarski (1993). Robust estimation in the Cox regression model, Scand. J. Statist. 20, 213-225.
  • T. Bednarski, S. Zontek (1996). Robust estimation of parameters in mixed unbalanced models, Ann. Statist. 24, 1493-1510.
  • Ch. Minder, T. Bednarski (1996). A robust method for proportional hazard regression, Statistics in Medicine 15, 1033-1047.
  • T. Inglot, W.C.M. Kallenberg, T. Ledwina (1998). Vanishing shortcoming of data driven Neyman's tests, in : Asymptotic Methods in Probability and Statistics, A Volume in Honour of Miklós Csörgő, North-Holland, 811-829.
  • K. Drosik, A. Michalski, S. Sadowski, A. Tukiendorf, R. Zmyślony (1998). Neoplasmatic Disease Incidence in Opole Province, Wydawnictwo Uniw. Opolskiego.
  • T. Bednarski, W. Florczak (1999). On a local uniform bootstrap validity, Statist. Neerl. 53, 111-121.
  • A. Janic-Wróblewska, T. Ledwina (2000). Data driven rank test for two-sample problem. Scand. J. Statist. 27, 281-297.
  • T. Inglot, W.C.M. Kallenberg (2003). Moderate deviations of minimum contrast estimators under contamination, An

Section of Applied Probability

The Section of Applied Probability stemmed from the Department of Applied Mathematics, one of the two basic departments of the State Mathematical Institute, which was founded on November 20, 1948. In 1950 this department was divided into two sections, one of them, the Section of Statistical Quality Control, was the predecessor of our section. According to the evolving interests of the members, this section was renamed the Industrial Applications Section in 1951, finally becoming the Applied Probability Section in 1973. In the period from 1950 to 1972 these sections were directed by Jan Oderfeld. At that time, the main focus was on statistical quality control, operations research and reliability theory. The section was headed by Robert Bartoszyński, Ryszard Zieliński and Tomasz Rychlik in the periods 1972-1985, 1985-2002 and 2002-2004, respectively. In the early seventies, the scientific interests of the group switched to probabilistic modelling (mostly, but not only, of biological phenomena), controlled Markov chains, stochastic approximation and random search. In recent years, various issues of mathematical statistics, including robust statistics, fixed precision estimation and moment bounds have become major focuses of the section's research.

The section was active in the organization of courses in applied mathematics, enhancing education in a wide spectrum of applied probability. Also, starting from 1971, Eugeniusz Fidelis annually organized the very popular National Conferences on Applications of Mathematics. Members of the group organized many international conferences in statistics, including Banach Center Semesters on Mathematical Statistics (1976) and Sequential Methods in Statistics (1981), among others.

Selected publications:

  • J. Oderfeld (1951). On the dual aspects of sampling plans. Colloq. Math. 2, 89-97.
  • R. Bartoszyński (1961). A characterization of the weak convergence of measures. Ann. Math. Statist. 32, 561-576.
  • J. Oderfeld, E. Pleszczyńska (1961). A linear estimate of the mean deviation in normal population [in Polish], Zastosow. Mat. VI, 111-117.
  • E. Fidelis, J. Oderfeld (1962). Two-step control taking into account the measurement errors [in Polish], Zastosow. Mat. VI, 249-256.
  • W. Rudzki (1962). Estimation of mean properties of shapeless products [in Polish], Zastosow. Mat. VI, 235-248.
  • R. Bartoszyński (1967). Branching processes and the theory of epidemics, Proc. Fifth Berkeley Symp. on Math. Statist. Probab. IV, 615-618.
  • E. Pleszczyńska (1973). Trend estimation problems in time-series analysis. Dissertationes Math. (Rozprawy Mat.) 104.
  • R. Zieliński (1973). A new class of estimators with an application to statistical quality control. Zastosow. Mat. XIII, 279-300.
  • R. Bartoszyński (1974). On a metric structure derived from subjective judgements: scaling under perfect and imperfect discrimination, Ecomometrica 42, 55-71.
  • R. Bartoszyński (1975). On risk of rabies, Math. Biosci. 24, 357-377.
  • R. Zieliński (1977). Global stochastic approximation. Dissertationes Math. (Rozprawy Mat.) 142.
  • R. Bartoszyński, W.J. Bühler (1978). On survival in hostile environment, Math. Biosci. 38, 293-301.
  • R. Bartoszyński, B.W. Brown, C.M. McBridge, J.R. Thompson (1981). Some nonparametric techniques for estimating the intensity function of a cancer related to nonstationary Poisson process. Ann. Statist. 9, 150-160.
  • R. Zieliński (1983). Robust statistical procedures: a general approach, in: ``Stability Problems for Stochastic Models'' (V.V. Kalashnikov and V.M. Zolotarev, eds.), Lecture Notes in Mathematics 982, Springer-Verlag, Berlin, 283-295.
  • B. Gołdys, M. Męczarski, R. Zieliński (1986). An asymptotic fixed-precision confidence interval for the minimum of a quadratic regression function. Probab. Math. Statist. 7, 7-11.
  • J. Koronacki, W. Wertz (1988). A global stopping rule for recursive density estimators. J. Statist. Plann. Inference 20, 23-39.
  • J. Koronacki (1989). Stochastic Approximation. Optimization Methods under Random Conditions [in Polish]. WNT, Warsaw.
  • B. Gołdys (1990). Regularity properties of solutions to stochastic evolution equations, Colloq. Math. 58, 327-338.
  • R. Rempała. (1990). Impulsive control problems. In: System Modelling and Optimization, Proceedings of the IFIP-Conference (Leipzig, 1989), (H.-J. Sebastian, K. Tammer, eds.), Lecture Notes in Control and Inform. Sci., Springer-Verlag, Berlin, 387-393.
  • R. Rempała (1991). Forecast horizon in a dynamic family of one-dimensional control problems, Dissertationes Math. (Rozprawy Mat.) 315.
  • R. Zieliński (1991). Fixed precision estimation in the Blum-Rosenblatt time series. Amer. J. Management Sci. 11, 233-239.
  • T. Rychlik (1993). Bounds for expectation of L-estimates for dependent samples, Statistics 24, 1-7.
  • L. Gajek, D. Zagrodny (1995). Geometric mean value theorems for the Dini derivative. J. Math. Anal. Appl. 191, 56-76.
  • W. Niemiro (1995). Estimation of nuisance parameters for inference based on least absolute deviations. Zastosow. Mat. 22, 515-529.
  • W. Niemiro, P. Pokarowski (1995). Tail events of some nonhomogeneous Markov chains, Ann. Appl. Probab. 5, 261-293.
  • L. Gajek, T. Rychlik (1996). Projection method for moment bounds on order statistics from restricted families. I. Dependent case. J. Multivar. Anal. 57, 156-174.
  • L. Gajek, T. Rychlik (1998). Projection method for moment bounds on order statistics from restricted families. II. Independent case. J. Multivar. Anal. 64, 156-182.
  • R. Zieliński (1998). Uniform strong consistency of sample quantiles. Statist. Probab. Lett. 37, 115-119.
  • T. Rychlik (2001). Projecting Statistical Functionals. Lecture Notes in Statistics 160, Springer-Verlag, New York.
  • S. Bylka, R. Rempała (2003). Selected Problems in the Mathematical Inventory Theory [in Polish], Akademicka Oficyna Wydawnicza Exit, Warsaw.

Mapa strony | Linki | Prawa autorskie

Copyright © 2006 by IMPAN. All rights reserved.