Department of Mathematical Statistics
About the Department
The Section of Mathematical Statistics was established on
April 1, 2004, as a unification of Section of
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
Przemysław Biecek, Katarzyna Danielak,
Tadeusz Inglot, Teresa Ledwina, Ryszarda Rempała,
Tomasz Rychlik, Grzegorz Wyłupek and Ryszard Zieliński.
The main scientific interests have been focused on the
- 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.
- 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, 1162-1169.
- 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.
- P. Jaworski, T. Rychlik (2008). On distributions of order statistics for
absolutely continuous copulas with applications to reliability
problems, Kybernetika 44, 757--776.
- G. Wyłupek (2010). Data driven k sample tests, Technometrics 52,
- T.Ledwina, J. Mielniczuk (2010). Variance function estimation via model selection,
Appl. Math. 37, 387-411.
- J. Navarro, T. Rychlik (2010). Comparisons and bounds for expected lifetimes of reliability systems,
Europ. J. Operational Res. 207, 309-317.
- K. Jasiński, T. Rychlik (2012). Bounds on dispersion of order ststistics based on dependent symmetrically
distributed random variables, J. Statist. Plann. Inf. 142, 2421-2429.
- T. Ledwina, G. Wyłupek (2012). Two-sample test against one-sided alternatives, Scand. J. Statist. 39, 358-381.
- Asymptotic Statistics (T. Inglot, T. Ledwina; Wrocław),
- Mathematical Statistics and other Probabilistic Applications
(M. Męczarski, J. Mielniczuk - until June 2010, P. Jaworski - since October 2010, T. Rychlik; Warszawa),
- Mathematical Statistics (W. Niemiro, T. Rychlik; Toruń, since 2008),
- Statistics in Medicine (P. Biecek; Wrocław, 2007-2008).
The Section of Mathematical Statistics and Its Applications stemmed from the Department of Applied Mathematics
of the State Institute of Mathematics, which was established in November 20, 1948.
In 1949 the Department consisted of six sections. Two of them: the General Section of Applications,
headed by Hugo Steinhaus, and the Section of Technical Applications, directed by Jan Mikusiński,
were located in Wrocław. These two sections formed later on the Section of Applications to Biology,
Economics and Technology, 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 journal Zastosowania Matematyki
(the subtitle Applicationes Mathematicae added in 1965), 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.
The journal is currently published as Biometrical Letters.
From 1968 to 1991 the Section was headed by Witold Klonecki and was renamed to 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. Symposium to honour
Jerzy Neyman (1974), 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.
- K. Florek, J. Łukaszewicz, J. Perkal, H. Steinhaus, S. Zubrzycki (1951). Sur la liaison et la division des points d'un ensemble fini, Colloq. Math. 2, 282-285.
- H. Steinhaus (1953/1954). On establishing paternity [in Polish], Zastosow. Mat. I, 67-82.
- A. Zięba (1953/1954). Elementary theory of pursuit [in Polish], Zastosow. Mat. I, 273-298.
- S. Drobot, M. Warmus (1954). Dimensional analysis in sampling inspection of
merchandise, Dissertationes Math. [Rozprawy Mat.] V.
- S. Gładysz, A. Rybarski (1954/1956). On modelling three-dimensional fields by a plane field of current [in Polish], Zastosow. Mat. II, 150-160.
- S. Zubrzycki (1954/1956). On the optimal method of water meter acceptance [in Polish], Zastosow. Mat. II, 199-209.
- A. Huskowska (1954/1956). On the accuracy of some natural science measurements, [in Polish], Zastosow. Mat. II, 426-430.
- J. Battek, J. Perkal (1956/1958). Quality and shape of forest stands [in Polish], Zastosow. Mat. III, 285-306.
- J. Łukaszewicz, M. Warmus (1956). Numerical and Graphical Methods [in Polish], PWN, Warszawa.
- S. Paszkowski i M. Warmus (1956). On some mathematical method in anthropology [in Polish],
Przegląd Antropologiczny XXII, 627-650.
- H. Steinhaus (1957). The problem of estimation, Ann. Math. Statist. 28, 633-648.
- S. Zubrzycki (1957). On estimating gangue parameters [in Polish], Zastosow. Mat. III, 105-153.
- E. Marczewski, H. Steinhaus (1958/1959). On the systematic distance of biotopes, [in Polish], Zastosow. Mat. IV, 195-203.
- H. Steinhaus, S. Trybuła (1958/1959). Measurement by successive comparison [in Polish], Zastosow. Mat. IV, 204-212.
- H. Steinhaus, K. Urbanik (1959). Poissonsche Folgen (Leon Lichtenstein zum Gedáchtnis), Math. Zeitsch. 72, 127-145.
- 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.
- S. Trybuła (1961). On the paradox of three random variables, Zastosow. Mat. V, 321-332.
- A. Bartkowiakowa, B. Gleichgewicht (1962). On the syllable characteristic of the Polish language [in Polish], Zastosow. Mat. VI, 309-319.
- A. Krzywicki, A. Rybarski (1962). On a linearization of an equation of an elastic rod, Zastosow. Mat. VI, 321-332.
- J. Perkal (1962). A design for a genetic test [in Polish], Zastosow. Mat. VI, 257-285.
- H. Steinhaus (1963). Probability, credibility, possibility, Zastosow. Mat. VI, 341-361.
- L. Zubrzycka (1963). On the adaptation of the typewriter keyboard to the structure of the language [in Polish], Zastosow. Mat. VI, 419-439.
- K. Florek (1964). On a certain method of graphical integration and graphical harmonic analysis, Zastosow. Mat. VII, 353-370.
- B. Kopociński, L. Zubrzycka (1964). Remark on division of systems of features into harmonized subsystems [in Polish], Zastosow. Mat. VII, 317-321.
- S. Zubrzycki (1966). Explicit formulas for minimax admissible estimators in some cases of restrictions imposed on the parameter, Zastosow. Mat. IX, 31-52.
- B. Bednarek-Kozek (1973). On estimation in the multidimensional Gaussian model, Zastosow. Mat. XIII, 511-520.
- H. Drygas, J. Srzednicka (1976). A new result on Hsu's model on regression analysis, Bull. Acad. Polon. Sci., Sér. Sci. Math. Phys. Astronom. 24, 1133-1136.
- S. Gnot (1976). The mean efficiency of block designs, Math. Operationsforsch. Statist. 7, 75-84.
- W. Klonecki (1977). Optimal C($\alpha$) tests for homogeneity, in : Proceedings of the Symposium to honour Jerzy Neyman (Warsaw 1974), PWN, 161-175.
- 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.
- W. Wawrzyniak (1981). A characterization of minimum variance unbiased estimators in the general linear model with restrictions on parameter space. Math. Operationsforsch. Statist. Ser. Statist. 12, 456-477.
- T. Bednarski (1982). Binary experiments, minimax tests and 2-alternating capacities, Ann. Statist. 10, 226-232.
- A.S. Kozek (1982). Towards a calculus for admisibility, Ann. Statist. 10, 825-837.
- S. Gnot, J. Kleffe, R. Zmyślony (1985). Nonnegativity of admissible invariant quadratic estimates in mixed linear models with two variance components, J. Statist. Plann. Inference 12, 249-258.
- 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.
- K. Drosik, A. Michalski, S. Sadowski, A. Tukiendorf, R. Zmyślony (1998). Neoplasmatic Disease Incidence in Opole Province, Wydawnictwo Uniw. Opolskiego.
- 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.
- T. Bednarski, W. Florczak (1999). On a local uniform bootstrap validity, Statist. Neerl. 53, 111-121.
- W.C.M. Kallenberg, T. Ledwina (1999). Data driven rank tests for independence,
J. Amer. Statist. Assoc. 94, 285-301.
- A. Janic-Wróblewska, T. Ledwina (2000). Data driven rank test for two-sample problem. Scand. J. Statist. 27, 281-297.
- T. Inglot, T. Ledwina (2001). Intermediate approach to comparison of
some goodness-of-fit tests, Ann. Inst. Statist. Math. 53, 810-834.
- G.R. Ducharme, T. Ledwina (2003). Efficient and adaptive nonparametric test for the two-sample problem, Ann. Statist. 31, 2036-2058.
- T. Inglot, W.C.M. Kallenberg (2003). Moderate deviations of minimum contrast estimators under contamination, Ann. Statist. 31, 852-879.
The Section of Applied Probability originated in a long process rooted in
the Department of Applied Mathematics of the State Mathematical Institute,
founded in 1948. Two Warsaw's sections of this department were forerunners of it. Namely,
the Section of Statistical Quality Control and the Actuarial Section.
In accordance with the evolving
interests of the members, the Section of Statistical Quality Control was renamed
to the Industrial Applications
Section in 1962. In the period from 1952 to 1970 these sections were directed
by Jan Oderfeld, with short break in 1959 when Czesław Rajski was in charge of it.
At that time, the research was mainly focused on statistical quality control, operations
research and reliability theory. The Actuarial Section evolved into the Section of
In 1951, Oskar Lange was put in charge of the section and he did it until 1958.
In 1958-1960 Marek Fisz was the leader of
it while later on the section was headed by Wiesław Sadowski.
Interests of the group were focused on statistics, decision making and
These two evolving groups were the predecessors the Applied Probability Section,
formally founded in 1972.
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,
a wide spectrum of applied probability. Also, starting from 1971, Eugeniusz
annually organized the very popular
National Conferences on Applications of Mathematics. Members of the group
organized many international conferences in statistics, including Banach Center
Mathematical Statistics (1976) and Sequential Methods in Statistics (1981), among
- J. Oderfeld (1951). On the dual aspects of sampling plans. Colloq. Math. 2, 89-97.
- M. Fisz (1954). Probability Theory and Mathematical Statistics (first edition; in Polish), PWN.
- T. Czechowski, W. Sadowski, W. Zasępa (1954/1956).
On determining the safety factor [in Polish], Zastosow. Mat. 2, 190-198.
- W. Sadowski (1954/1956). On a non-parametric test of comparing dispersions [in Polish],
Zastosow. Mat., 2, 161-171.
- C. Rajski (1954/1956). On the verification of hypotheses concerning two populations
consisting of items marked by attributes [in Polish], Zastosow. Mat., 2, 179-189.
- M. Fisz, K. Urbanik (1956). Analytical characterization of the composed non-homogeneous
Poisson process, Stud. Math. 15, 328-336.
- M. Fisz (1958). A limit theorem for empirical distribution functions,
Stud. Math. 17, 71-77.
- O. Lange (1959). Introduction to Econometrics (first edition; in Polish), PWN.
- J. Łukaszewicz, Sadowski, W. (1960/1961). On comparing several populations with a
control population . Zastosow. Mat. 5, 309-320.
- 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.)
- R. Bartoszyński, W.J. Bühler (1978). On survival in hostile environment, Math. Biosci.
- 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,
- 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 (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
- 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.