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1 Evgeny Slutsky Collected Statistical Papers Selected and Translated by Oscar Sheynin Assisted by Guido Rauscher and Claus

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1 Evgeny Slutsky Collected Statistical Papers Selected and Translated by Oscar Sheynin Assisted by Guido Rauscher and Claus Evgeny Slutsky Collected Statistical Papers Selected and Translated by Oscar Sheynin Assisted by Guido Rauscher and Claus Wittich Berlin, 2010 ISBN 3-938417-82-X © Oscar Sheynin, 2010 www.sheynin.de 1 Contents Foreword I. Theory of Correlation and Elements of the Doctrine of the Curves of Distribution , 1912. Foreword II. Statistics and mathematics, 1916 III. On the logical foundation of the calculus of probability, 1922 IV. On some patterns of correlation connection and the systematic error of the correlation coefficient, 1923 V. On a new coefficient of mean density of population, 1923 VI. On calculating the state revenue from the emission of paper money, 1923 VII. Mathematical notes on the theory of emission, 1923 VIII. On the law of large numbers, 1925 IX. Al. Tschuprow, 1926 X. On the distribution of errors [on the law of distribution] of the correlation coefficient in homogeneous connected series, 1932 XI. On the existence of connection between the solar constant and temperature, 1933 XII. On the solar constant, 1934 XIII. On the eleven year periodicity of sunspots, 1935 XIV. Statistical experiment as a method of investigation. Critical notes on the problem Earth – Sun, 1935 XV. G. Rauscher, O. B. Sheynin, C. Wittich, The correspondence between E. E. Slutsky and V. I. Bortkevich, 2007 XVI. Autobiography, 1939 XVII. Autobiography, 1942 XVIII. O. Sheynin, Slutsky: Commemorating the 50 th anniversary of his death, 1999 XIX. N. S. Chetverikov, The life and scientific work of E. E. Slutsky, 1959 XX. B. V. Gnedenko, N. V. Smirnov, Foreword to Slutsky’s Selected Works , 1960 2 Foreword 1. General Information 1.1. For a first approximation to Evgeny Evgenievich Slutsky’s (1880 – 1948) biography see [xix]. I have also included other materials about him [xviii]; [xx] and his own autobiographies [xvi; xvii], regrettably very short. Among obituaries I single out those written by Kolmogorov and Smirnov, both in 1948 and quoted by Chetverikov [xix]. Much information about Slutsky is contained in several Russian archives and still largely unstudied. Slutsky was an outstanding scholar remembered for his achievements in economics, statistics and theory of probability. As an economist, he enjoys worldwide renown as one of the forerunners of econometrics (Zarkovitch 1956, p. 338/1977, p. 484). See [xv, Note 20]. Slutsky saw that his economic studies became impossible; mathematical methods had only entered Soviet economics in the 1960s, and, for that matter, with great difficulties; the Conjuncture Institute, where he had been a consultant, was shut down and statisticians in general became muzzled (Sheynin 1998; 2008, pp. 365 – 367); theological issues seriously interested him, but he could only discuss them with relatives and closest friends. In other words, he had been experiencing the usual fate (by far not its worst possible version) of the Soviet intelligentsia. Theoretical statistics was Slutsky’s stepping stone to probability; moreover, two of his papers here included [iii; viii] were devoted to the theory of probability, but at least chronologically they belong to the statistical period of Slutsky’s life and directly bear on statistics. Two papers [vi; vii] treated the emission of paper money, and one [v] dwelt on the density of population, both subjects important but rarely discussed by statisticians. Also important were his studies of the correlation theory. In applications, he considered as most fruitful his geophysical contributions [xvi], but later he [xvii] stated that the appropriate period of his life was definitively lost owing to the impossibility of carrying out comprehensive studies. I believe that the loss was only comparative, with respect to what was possible under more favourable conditions. Incidentally he many times expressed his (failed) intentions to further his work in the same direction. And I ought to stress that during the statistical period of his life, Slutsky remained one of the very few leading Soviet statisticians and that he time and time again referred to Chuprov, officially considered a scholar refusing to return to Russia. At the same time, Slutsky invariably calculated and provided his numerical results with superfluous (and therefore dangerous) digits. I [vii, Note 5] remarked on the most glaring example of this habit. Other unpleasant features are insufficient and sometimes careless explanation of his subject and the really bad, and again sometimes carelessly written English summaries to his geophysical papers. In spite of the above, calculations were Slutsky’s strong point which is clearly seen in his geophysical works. Here is Kolmogorov’s pertinent opinion (1948/2002, p. 71): Slutsky was Not embarrassed by corrupting the purity of his method [of solving problems when the analytic approach had failed]. If tables became necessary , […] he was prepared to spend years compiling them . 3 Kolmogorov certainly meant Slutsky’s noteworthy contribution, the table of the Γ-function. From time to time, and especially at anniversaries of the October (old style) 1917 coup d’état, essays on the state of various sciences were being published. I (2005) have collected translations of such contributions on probability and statistics, and it is not difficult to find there many references to Slutsky. Kolmogorov, in 1935, 1938 and 1948 stressed the importance of his work on random functions and placed him alongside Wiener and Lévy (in 1935), and together with himself in 1938. In 1948, in a joint publication with Gnedenko, he repeated the latter statement and singled out Slutsky (1937). Then, in 1947, Kolmogorov named Khinchin, himself and Slutsky as the originators of the Moscow school of probability. Smirnov, in 1948 (not in the obituary of the same year) stated that Slutsky, Khinchin and Kolmogorov largely created the theory of continuous stochastic processes and Gnedenko, in 1970, noted that Bernstein and Slutsky were the first Soviet authors on the theory of probability and mathematical statistics. The tradition of publishing fundamental essays had a horrible ideological aspect. Thus, Khinchin (1937), of all men, wrote a servile contribution falsely describing the situation of science in pre-revolutionary Russia and comparing it with the alleged splendid position of the day, and that at the time when the Great Terror was in full swing! Acknowledgement. It is my pleasant duty to mention Magister Guido Rauscher (Vienna) and Dr. Claus Wittich (Geneva). All three of us jointly published [xv] and it was G. R. who had discovered the Bortkiewicz papers (including his correspondence with Slutsky) in Uppsala. He had also found out that important and still largely unstudied material concerning Slutsky is kept in RGALI (Russian State Archive for Literature and Arts). Claus Wittich partly edited my translation of [vi] and sent me the text of [xiii]; incidentally, that contribution had appeared both in Russian and English, and I have just reprinted the English version. I have also profited from two of his unpublished texts of 2005 and 2007 which he put at my disposal, Biographical notes on, and Bibliographical notes on selected sources concerning Slutsky. I will now formulate some comments on most of the included papers. References to literature mentioned there are included in the Bibliographies to those papers, but I am providing the information about the sources mentioned above right now: Khinchin A. Ya. (1937), The theory of probability in pre-revolutionary Russia and in the Soviet Union. Front Nauki i Tekhniki , No. 7, pp. 36 – 46. Translation: Sheynin (2005, pp. 40 – 55). Sheynin, O. (1998), Statistics in the Soviet epoch. Jahrbücher f. Nationalökonomie u. Statistik , Bd. 217, pp. 529 – 549. ---, compiler and translator (2005), Probability and Statistics. Soviet Essays . Berlin. Also at www.sheynin.de --- (2008), Romanovsky’s correspondence with K. Pearson and R. A. Fisher. Archives Intern. d’Histoire des Sciences , t. 58, No. 160 – 161, pp. 365 – 384. Slutsky E. (1937), Quelche propositione relative alla teoria delle funzioni aleatorie. Giorn. dell. Istituto Italiano degli Attuari , t. 8, No. 2, pp. 3 – 19. Zarkovitch S. S. (1956), Note on the history of sampling methods in Russia. J. Roy. Stat. Soc. , vol. A119, pp. 336 – 338. Reprinted in Kendall M., Plackett R. L. (1977), Studies in the History of Statistics and Probability , vol. 2. London, pp. 482 – 484. 4 1.2. Comments on Separate Papers [iii] Kolmogorov (1948/2002, p. 69) stated that Slutsky “was the first to draw a correct picture of the purely mathematical essence of probability theory” and cited the paper here translated (“the present paper”, as I shall call it) and a later contribution (Slutsky 1925). Earlier, Kolmogorov (1933) referred to both these articles but did not mention the former in the text itself; curiously enough, that inconsistency persisted even in the second Russian translation of Kolmogorov’s classic published during his lifetime (Kolmogorov 1974, pp. 54 and 66). Several years after 1922 Slutsky [viii, Note 2] remarked that back then he had not known Bernstein’s work (1917) which “deserves a most serious study”. In his Commentary, B. V. Gnedenko (Slutsky 1960, p. 284) most approvingly cited a passage here intalicized in § 5 and, on p. 285, concluded that Slutsky had Correctly and deeply (and apparently for the first time) approached the construction of the theory of probability in a rigorous and purely mathematical way. His paper played an important part in forming contemporary ideas about the foundations of the theory of probability and occupies a noticeable place in its history . This English translation of [iii] first appeared in Sheynin (2005). [iv] In a letter of 1924 to Chetverikov, Chuprov (Sheynin 1990/1996, p. 49) commented: I have recently received from Slutsky reprints of his papers. For me, the work [the present article] is very interesting; both in its approach and in the results obtained it accords with what I had arrived at for the correlation coefficient . There seems to be no investigation of the systematic error of that coefficient in Chuprov’s published works; however, Slutsky himself several times referred to Chuprov and Chuprov (1923, Appendix) contains all the formulas from the beginning of § 3 to (7) inclusively.
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