Norbert Schmitz (mathematician)

from Wikipedia, the free encyclopedia
Norbert Schmitz 2006

Norbert Schmitz (born August 27, 1939 in Münster , Westphalia ) is a German mathematician specializing in stochastics and business mathematics .

Live and act

From 1958 to 1964 Schmitz studied at the University of Munich and the University of Münster , where he received the diploma and passed the first state examination on a topic set by Dietrich Morgenstern (Freiburg). He then worked at the Institute for Mathematical Statistics at the University of Münster. After receiving his doctorate in 1966 (with the dissertation “Treatment of a symmetrical multiple decision problem” supervised by Hermann Witting ), he moved to the University of Karlsruhe (TH) as an assistant to Dietrich Bierlein . There he completed his habilitation in 1970 with the text “Sequential Tests at given levels”.

After a substitute for a chair in Karlsruhe, he accepted a professorship at the Free University of Berlin in the autumn of 1970 . In 1972 he was offered professorships for mathematical statistics at the University of Konstanz and the University of Münster as well as at RWTH Aachen University ; he went to the Westphalian Wilhelms University of Münster as the successor to Hermann Witting. There he remained despite a call to the Technical University of Munich (1976) until his retirement in 2004.

Schmitz's main areas of work were sequential analysis, where he developed the sequentially planned tests, mathematical game theory , simulation methods ( Monte Carlo methods ) and mathematical economic theory . After his retirement, he devoted himself to the history of science.

Fonts

Selected books
  • together with Detlef Plachky: Lectures on Probability Theory I. Mathematical Systems in Economics, Volume 26, Meisenheim: Hain, 1976
  • together with Fritz Lehmann: Monte Carlo Methods I: Generating and testing random numbers. Mathematical Systems in Economics, Volume 28, Meisenheim: Hain, 1976 (2nd edition Münster 1982)
  • together with Burkhard Rauhut and Ernst-Wilhelm Zachow: Game theory. Stuttgart: Teubner, 1979
  • Optimal Sequentially Planned Decision Procedures. Lecture Notes in Statistics. Vol. 79. New York: Springer, 1992 (2nd edition 1993)
  • Lectures on probability theory. Stuttgart: Teubner, 1996
  • together with Friedrich Harten, and Andreas Meyerthole: Prophet theory: prophet inequalities, prophet regions , games against a prophet. Stuttgart: Teubner, 1997
  • Stochastics for student teachers, Münster: LIT-Verlag, 1997
  • together with Jürgen Elstrodt : History of Mathematics at the University of Münster; Part I: 1773–945 Münster, 2008 (online)
  • 1959–2009: 50 years of the Institute for Mathematical Statistics at the Westphalian Wilhelms University of Münster, Münster, 2009 [1]
  • Adolf Kratzer 1893–1983, Münster: Monsenstein and Vannerdat, 2011 (online)
Selected items
  • For the construction of consistently best minimax processes with multiple decision problems. Unternehmensforschung 12 (1968), pp. 34-49
  • Likelihood quotient sequence tests on homogeneous Markoff chains. Biometric Journal 10 (1968), 231-247
  • Sequential Minimax tests in Wiener processes. Z. Math. Operationsforschung und Statistik 1 (1970), 289-295
  • Existence of sequential tests at given levels. Archive of Mathematics XXI (1970/71), 617–628
  • A note on the optimality of k-stage tests. Metrika 19: 72-75 (1972)
  • together with Albrecht Irle : Decision Theory for Continuous Observations I: Bayes-Solutions. Transactions Seventh Prague Conference on Information Theory, Stat. Decision Funct. and Random Processes (1974), Prague 1977, 209-221
  • A Further Note on Arrow's Impossibility Theorem. J. of Mathematical Economics 4: 189-196 (1977)
  • together with Albrecht Irle : On the optimality of the SPRT for processes with continuous time parameter. Mathematical operations research and statistics; Ser. Statistics 15: 91-104 (1984).
  • together with Gerti Kohlruss: Extremal distributions for the prophet Region in the independent case. Annals of Operations Research, 32: 115-126 (1991).
  • together with Marion Harenbrock: Optional Sampling of Submartingales with Scanned Index Sets. Journal Theor. Prob. 5 (1992); 309-326.
  • together with Bhaskar Kumar Ghosh : Best linear unbiased estimation of the population mean under sequential sampling. Sankya, Ser. B; 58: 184-198 (1996)
  • together with Jens Gebhard: Permutation tests - A revival ?! I. Optimum properties. / II. An efficient algorithm for computing the critical region. Statistical Papers 39: 75-85 / 87-96 (1998)
  • together with Annemarie Hawix: Remarks on the modified Kiefer-Weiss problem for exponential families. Sequential Analysis 17: 297-303 (1998)
  • together with Andreas Meyerthole: Games against a Prophet for Stochastic Processes. In: Game Theory, Optimal Stopping, Probability and Statistics (Eds. Thomas Bruss / Lucien Le Cam ). Inst. Of Math. Statistics Lecture Notes-Monograph Series Vol. 35 (2000), 53-69
  • together with Dominik Völker: Nonparametric optimality properties of optimal parametric tests. Statistical Archive 87 (2003); 353-367
  • together with Hendrik Kläver: An Inequality for the Asymmetry of Distributions and a Berry-Esseen Theorem for Random Summation. Journal of Inequalities in Pure and Applied Mathematics 7 (2006), (2), 1-12

Web links

personal data
SURNAME Schmitz, Norbert
ALTERNATIVE NAMES Schmitz, Norbert J.
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH August 27, 1939
PLACE OF BIRTH Munster (Westphalia)