Abstract
The word “statistics” originated from the Latin word “status” and according to Kendall and Stuart (The Advanced Theory of Statistics. Vol. 1. Distribution Theory, Hafner Publishing Co., New York (1958)) “Statistics is the branch of scientific method which deals with the data obtained by counting or measuring the properties of populations”. So the main task of Statistics is to collect data and make conclusions, usually called Statistical Inference. Thus statistical methods have been used for a long time also in Hungary, e.g., in Hungarian Central Statistical Office founded in 1867 and also in other organizations. The data are usually subject to random fluctuations and so the theory of statistical inference should be based on rigorous mathematical concepts treating random phenomena, i.e., on the Theory of Probability. Mathematical Statistics is the theory of statistical methods based on rigorous mathematical concepts of Probability. In this way we can consider Károly (Charles) Jordan as the founder of the probability and statistics school in Hungary, who wrote the first book on Mathematical Statistics in Hungary.
Supported by the Hungarian National Foundation for Scientific Research, Grant No. T 029621 and T 037886.
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References
Jordan, Károly, Matematikai Statisztika (Mathematical Statistics), Természet és Technika, Volume 4, Athenaeum (Budapest, 1927, in Hungarian), and Statistique mathématique, Gauthier-Villars (Paris, 1927, in French).
Wald, Abraham, Sequential Analysis, John Wiley and Sons (New York) — Chapman and Hall (London, 1947).
V. André, Solution directe du problème résolu par M. J. Bertrand, CR. Acad. Sei. Paris, 105 (1887), 436–437.
E. Barbier, Généralisation du problème résolu par M. J. Bertrand, CR. Acad. Sei. Paris, 105 (1887), 407.
M. J. Bertrand, Solution d’un problème, CR. Acad. Sei. Paris, 105 (1887), 369.
Z. W. Birnbaum and I. Vincze, Limiting distributions of statistics similar to Student’s t, Ann. Statist, 1 (1973), 958–963.
F. P. Cantelli, Sulla determinazione empirica délie leggi di probabilità, Giorn. 1st. Rai. Attuari, 4 (1933), 421–424.
K. L. Chung and W. Feller, Fluctuations in coin tossing, Proc. Nat. Acad. Sei. USA, 35 (1949), 605–608.
H. Cramér, Mathematical Methods of Statistics, Princeton University Press (Princeton, 1946).
E. Csáki and I. Vincze, On some problems connected with the Galton test, Publications of the Math. Inst. Hung. Acad. Sei., 6 (1961), 97–109.
E. Csáki and I. Vincze, Two joint distribution laws in the theory of order statistics, Mathematica, Cluj 5 (1963), 27–37.
E. Csáki and I. Vincze, On limiting distribution laws of statistics analogous to Pearson’s chi-square, Mathematische Operationsforschung und Statistik, Ser. Statistics, 9 (1978), 531–548.
A. Dvoretzky, A. Wald and J. Wolfowitz, Elimination of randomization in certain statistical decision procedures and zero-sum two-person games, Ann. Math. Statist., 22 (1951), 1–21.
M. Fréchet, Sur l’extension de certaines évaluations statistiques au cas de petits échantillons, Rev. Inst Internat. Statist., 11 (1943), 182–205.
V. Glivenko, Sulla determinazione empirica delle leggi di probabilità, Giorn. Ist. Rai. Attuari, 4 (1933), 92–99.
B. V. Gnedenko and V. S. Korolyuk, On the maximum discrepancy between two empirical distribution functions, Dokl. Akad. Nauk SSSR, 80 (1951), 525–528; English translation: Selected Transi. Math. Statist. Probab., Amer. Math. Soc., 1 (1951), 13-16.
Z. Govindarajulu and I. Vincze, The Cramér-Fréchet-Rao inequality for sequential estimation in non-regular case, Statistical Data Analysis and Inference (Ed. Y. Dodge), North Holland (Amsterdam, 1989), 257–268.
B. Gyires, On limit distribution theorems of linear order statistics, Publ. Math. Debrecen, 21 (1974), 95–112.
B. Gyires, Linear order statistics in the case of samples with non-independent elements, Publ. Math. Debrecen, 22 (1975), 47–63.
B. Gyires, Jordan Károly élete és munkássága, Alkalmazott Matematikai Lapok, 1 (1975), 274–298.
B. Gyires, Normal limit-distributed linear order statistics, Sankhyã, Ser. A 39 (1977), 11–20.
B. Gyires, Linear rank statistics generated by uniformly distributed sequences, Colloq. Math. Soc János Bolyai 32, North-Holland (Amsterdam, 1982), 391–400.
B. Gyires, Doubly ordered linear rank statistics, Acta Math. Acad. Sei. Hungar., 40 (1982), 55–63.
G. Hajós and A. Rényi, Elementary proofs of some basic facts in the theory of order statistics, Acta Math. Acad. Sei. Hung., 5 (1954), 1–6.
K. Jordan, A valoszfniiség a tudományban és az életben (Probability in science and life, in Hungarian), Természettudomdnyi Közlöny, 53 (1921), 337–349.
K. Jordan, On probability, Proceedings of the Physico-Mathematical Society of Japan, 7 (1925), 96–109.
K. Jordan, A valosziniiségszámitás alapfogalmai (Fundamental concepts of the theory of probability) Mathematikai és Physikai Lapok, 34 (1927), 109–136.
K. Jordan, Sur une formule d’interpolation Atti del Congresso Internazionale dei Matematici, Bologna, Vol. 6 (1928), 157–177.
C. Jordan, Approximation and graduation according to the principle of least squares by orthogonal polynomials, Ann. Math. Statist., 3 (1932), 257–357.
Ch. Jordan, Le théorème de probabilité de Poincaré, généralisé au cas de plusieurs variables indépendantes, Acta Scientiarum Mathematicarum (Szeged), 7 (1934–35), 103–111.
Ch. Jordan, Problèmes de la probabilité des épreuves répétées dans le cas général, Bull, de la Société Mathématique de France, 67 (1939), 223–242.
K. Jordan, Kovetkeztetések statisztikai észlelésekból (Statistical inference, in Hungarian), Magyar Tad. Akad. Mat. Fiz. Oszt. Kozleményei, 1 (1951), 218–227.
K. Jordan, Fejezetek a klasszikus valósziniiségszámitásból, Akadémiai Kiado (Budapest, 1956, in Hungarian), Chapters on the classical calculus of probability (1972, in English).
A. N. Kolmogorov, Sulla determinazione empirica di una legge di distribuzione, dorn. Ist. Ital. Attuari, 4 (1933), 83–91.
P. Kosik and K. Sarkadi, A new goodness-of-fit test, Probability Theory and Mathematical Statistics with Applications (Visegrád, 1985), Reidel (Dordrecht, 1988), 267–272.
H. B. Mann and A. Wald, On the choice of the number of class intervals in the application of the chi square test, Ann. Math. Statist., 13 (1942), 306–317.
M. L. Puri and I. Vincze, On the Cramér-Fréchet-Rao inequality for translation parameter in the case of finite support, Statistics, 16 (1985), 495–506.
C. R. Rao, Information and accuracy attainable in the estimation of statistical parameter, Bull. Calcutta Math. Soc, 37 (1945), 81–91.
J. Reimann and I. Vincze, On the comparison of two samples with slightly different sizes, Publications of Math. Inst. Hung. Acad. Sei, 5 (1960), 293–309.
A. Rényi, On the theory of order statistics, Acta Math. Acad. Sei. Hung., 4 (1953), 191–231.
K. Sarkadi, On testing for normality, Magyar Tud. Akad. Mat. Kutató Int. Közl, 5 (1960), 269–275.
K. Sarkadi, On Galton’s rank order test, Magyar Tud. Akad. Mat. Kutató Int. Közl, 6 (1961), 127–131.
K. Sarkadi, Proc. Fifth Berkeley Sympos. Math. Statist, and Probability I, Univ. California Press (Berkeley, Calif., 1967), 373–387.
K. Sarkadi, Estimation after selection, Studia Sei. Math. Hung., 2 (1967), 341–350.
K. Sarkadi, On the exact distributions of statistics of Kolmogorov-Smirnov type, Collection of articles dedicated to the memory of Alfred Rényi, II. Period. Math. Hungar., 3 (1973), 9–12.
K. Sarkadi, The consistency of the Shapiro-Francia test, Biometrika, 62 (1975), 445–450.
K. Sarkadi, A direct proof for a ballot type theorem, Colloq. Math. Soc. Jdnos Bolyai, 32, North-Holland (Amsterdam, 1982), 785–794.
N. V. Smirnov, On the empirical distribution function (in Russian), Mat. Sbornik, 6 (48) (1939), 3–26.
C. Stein and A. Wald, Sequential confidence intervals for the mean of a normal distribution with known variance, Ann. Math. Statist., 18 (1947), 427–433.
L. Takács, Charles Jordan, 1871–1959, Ann. Math. Statist, 32 (1961), 1–11.
L. Takács, Ballot problems, Z. Wahrsch. verw. Geb., 1 (1962), 154–158.
L. Takács, Fluctuations in the ratio of scores in counting a ballot, J. Appl. Probab., 1 (1964), 393–396.
L. Takács, Combinatorial Methods in the Theory of Stochastic Processes, Wiley (New York, 1967).
L. Takács, On maximal deviation between two empirical distribution functions, Studia Sei. Math. Hung., 10 (1975), 117–121.
I. Vincze, Statisztikai minoségellenorzés: az ipari minoségellenorzés matematikai statisztikai modszerei (Statistical quality control: The mathematical-statistical methods of industrial quality control, in Hungarian), Kozgazdasági és Jogi Könyvkiadö, Budapest (1958).
I. Vincze, Einige zweidimensionale Verteilungs-und Grenzverteilungssatze in der Theorie der geordneten Stichproben, Publications of the Math. Inst. Hung. Acad. Sei., 2 (1958), 183–209.
I. Vincze, On some joint distribution and joint limiting distribution in the theory of order statistics, II, Publications of the Math. Inst. Hung. Acad. Sei., 4 (1959), 29–47.
I. Vincze, Some questions connected with two sample tests of Smirnov type, Proc. of the Fifth Berkeley Symp. on Math. Stat and Prob., Univ. of Calif. Press Vol. 1 (1967), 654–666.
I. Vincze, On the power of the Kolmogorov-Smirnov two-sample test and related nonparametric tests, Studies in Mathematical Statistics, Publishing House of the Hung. Acad. Sei. (Budapest, 1968), 201–210.
I. Vincze, On some results and problems in connection with statistics of the Kolmogorov-Smirnov type, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, I, Univ. California Press (1972), 459–470.
I. Vincze, On the Cramér-Fréchet-Rao inequality in the non-regular case, Contributions to Statistics. Hdjek Memorial Volume, Academia (Prague, 1979), 253–262.
I. Vincze, On nonparametric Cramér-Rao inequalities, Order Statistics and Nonparametrics (Ed. P. K. Sen and I. A. Salama) North Holland (Amsterdam, 1981), 439–454.
J. von Neumann, Distribution of the ratio of the mean square successive difference to the variance, Ann. Math. Statist, 12 (1941), 367–395.
J. von Neumann, A further remark concerning the distribution of the ratio of the mean square successive difference to the variance, Ann. Math. Statist, 13 (1942), 86–88.
A. Wald, Contributions to the theory of statistical estimation and testing hypotheses, Ann. Math. Statist, 10 (1939), 299–326.
A. Wald, Asymptotically most powerful tests of statistical hypotheses, Ann. Math. Statist, 12 (1941), 1–19.
A. Wald, Asymptotically shortest confidence intervals, Ann. Math. Statist., 13 (1942), 127–137.
A. Wald, Tests of statistical hypotheses concerning several parameters when the number of observations is large, Trans. Amer. Math. Soc, 54 (1943), 426–482.
A. Wald, Sequential tests of statistical hypothesis, Ann. Math. Statist., 16 (1945), 117–186.
A. Wald, Some improvements in setting limits for the expected number of observations required by a sequential probability ratio test, Ann. Math. Statist., 17 (1946), 466–474.
A. Wald, Differentiation under the expectation sign in the fundamental identity of sequential analysis, Ann. Math. Statist, 17 (1946), 493–497.
A. Wald, Asymptotic properties of the maximum likelihood estimate of an unknown parameter of a discrete stochastic process, Ann. Math. Statist., 19 (1948), 40–46.
A. Wald, Estimation of a parameter when the number of unknown parameters increases indefinitely with the number of observations, Ann. Math. Statist., 19 (1948), 220–227.
A. Wald, Asymptotic minimax solutions of sequential point estimation problems, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press (1951), 1–11.
A. Wald, Selected Papers in Statistics and Probability by Abraham Wald, McGraw-Hill Bokk Company, Inc. (New York-Toronto-London, 1955).
A. Wald and J. Wolfowitz, On a test whether two samples are from the same population, Ann. Math. Statist, 11 (1940), 147–162.
A. Wald and J. Wolfowitz, An exact test for randomness in the nonparametric case based on serial correlation, Ann. Math. Statist, 14 (1943), 378–388.
A. Wald and J. Wolfowitz, Statistical tests based on permutations of the observations, Ann. Math. Statist, 15 (1944), 358–372.
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Csáki, E. (2006). Mathematical Statistics. In: Horváth, J. (eds) A Panorama of Hungarian Mathematics in the Twentieth Century I. Bolyai Society Mathematical Studies, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30721-1_16
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