Anderson, Oskar N.
Anderson, Oskar N.
Oskar Nikolayevich Anderson (1887–1960), a pioneer of applied sampling-survey techniques, and remembered also for his contributions to the variatedifference method, has been described as “perhaps the most widely known statistician in Central Europe. … He provided a link between the Russian school of statistics ... ([A.A.] Markoff [Sr.], Tschuprow) and the Anglo-American school. … Through his origin in the flourishing Russian school of ‘probabilistes,’ ... Anderson belongs to the socalled ‘continental’ school of statistics, and worked in the tradition of the well known German statisticians [W.] Lexis and [L.] von Bortkiewicz. He might be the last representative of this approach ...” (Tintner 1961, p. 273).
Anderson was born in Minsk, Byelorussia. His father was a professor of Finno–Ugric languages at the University of Kazan. Although the Andersons were Russian subjects, they were ethnically German. In 1906 Anderson was graduated from the gymnasium in Kazan with a gold medal. After studying mathematics at the University of Kazan for a year, he entered the economics department of the Polytechnical Institute in St. Petersburg. There he became an outstanding pupil of Aleksandr A. Chuprov (or Tschuprow), whose strong permanent influence on Anderson is evident, even in such detailed matters as taxonomic conventions. As B. I. Karpenko wrote: “The ideas of A. A. Chuprov penetrate into foreign science not only directly but also through the writings of his students ... e.g., O. N. Anderson, who wrote a series of valuable works, in particular a serious book on the theory of statistics, which (in German) expounds A. A. Chuprov’s ideas …” (Karpenko 1957, p. 317).
From 1912 to 1917 Anderson taught in a commercial gymnasium in St. Petersburg. While there he also obtained a law degree. In 1915 he took part in an expedition to Turkestan to make a survey of agricultural production under irrigation in the Syr Darya River area. There, as chief scientific consultant, Anderson made one of the earliest applications of sampling methods. It apparently had only one Russian precedent: on January 6, 1910, Chuprov had presented a paper on the application of sampling techniques to data from the 1898–1900 rural census, but this application had had an “experimental, rather than a practical, character” (Volkov 1961, p. 159).
In 1917 Anderson served as research economist for a large cooperative society in southern Russia and also underwent further training in statistics at the Commercial Institute in Kiev, where he became a docent in 1918. Concurrently, he held an executive position in the demographic institute of the Academy of Sciences in Kiev. While in Kiev, he came to know and was perhaps influenced by Eugen Slutsky.
Like many Russian students of his time, Anderson had leftist sympathies. In 1920, however, he and his family left Russia as a result of the political upheavals. The following year he became a high school principal in Budapest; from 1924 to 1933 he was a professor at the Commercial Institute in Varna, Bulgaria; and from 1935 to 1942 he held a similar position at the University of Sofia. From the mid-1920s on, he was a member of the Supreme Statistical Council of the Bulgarian government. He successfully advocated the use of sampling techniques—in addition to a complete enumeration —in the 1926 census of population and manufacture. Another large-scale sample survey instigated by Anderson covered Bulgarian agricultural production and producers in 1931–1932. In 1936 he began a complete redesigning of the acreage and crop statistics, basing them on purposive sampling.
In 1933 Anderson went to England and Germany on a Rockefeller stipend and, as a result of this trip, he published his first textbook (1935). He was a charter member of the Econometric Society. He contributed the article “Statistical Method” to the Encyclopaedia of the Social Sciences (1934). From the middle 1930s on, he served as an adviser for the League of Nations. In 1940 the Bulgarian government sent him to Germany, then at war, to study rationing. In 1942 Anderson accepted an appointment at the University of Kiel, Germany, and from 1947 to his death he was a professor of statistics in the economics department of the University of Munich. He was coeditor of the Mitteilungsblatt für mathematische Statistik (later Metrika) from its inception until he died. At the time of his death, his authority in German statistical circles was unrivaled. It was mainly through his efforts that the statistical training for economists at German universities was improved or was maintained at a reasonable level, despite various adverse influences.
Major contributions. One author has summed up Anderson’s lifework in the following manner: The course of outer events in Oskar Anderson’s life reflects the turbulence and agonies of a Europe torn by wars and revolutions. His scientific work, always marked by personal involvement, is of sufficient stature to be of lasting interest. … Some of Anderson’s endeavours were ahead of his time, along lines that have not yet received adequate attention. Thus his emphasis on causal analysis of nonexperimental data is a reminder that this important sector of applied statistics is far less developed than descriptive statistics and experimental analysis. … The main strength of Anderson’s scientific æuvre lies, I think, in the systematic coordination of theory and application. Only to a relatively small extent does his importance derive from specific contributions. … (Wold 1961, pp. 651–653)
Despite the cogent appraisal by Wold, it seems desirable to take up some of Anderson’s particular contributions.
Sample surveys. The Turkestan sample survey of 1915 and a demographic sampling study of 1916–1917 are contained in manuscripts that were lost; it seems safe to assume that the lost papers were valuable ones. We do have access to the first Bulgarian sample survey, which Anderson designed and whose implementation he supervised (1929a).
Variate-difference method in time series. Utilizing, in essence, the theorem that the nth difference of a polynomial of degree n is a constant and the (n + l)st zero, the variate-difference method attempts to analyze time series on the basis of few assumptions, but including the sensitive one that random errors are not autocorrelated. Anderson developed the method concurrently with William S. Gosset (for details, see Tintner 1940, pp. 10–15). The method has not met with general favor, although it is still taken as a point of departure for various theoretical studies. Anderson himself was aware of its limitations (1954, pp. 178–180 in 1957 edition). In a different context, his incisive critique of the Harvard method of time-series analysis (1929b) is recognized as having definitively discredited mechanical procedures of that kind.
Quantitative economics. Anderson’s study of the “verifiability” of the quantity theory of money (1931) is an econometric classic because Anderson took advantage of the then new awareness of the importance of random residuals. Several of his papers analyze the causes of divergent movements of agricultural and industrial prices. A critique of N. D. Kondratieff’s work on long waves (in business cycles) is among Anderson’s lost papers. His contributions to index-number theory were both constructive and critical. For reasons of error accumulation, he was specifically against chain indexing (1952).
Probability theory and nonparametric methods. Anderson’s was essentially an eclectic, and somewhat modified, frequency point of view (e.g. 1954, pp. 98–100 in 1957 edition). In particular, he felt that finite, rather than infinite, urn models were more appropriate in most social contexts; correspondingly, he was against too facile an invocation of the central-limit theorem. In his papers on nonparametric methods (1955a; 1955b), he intended to make correlation and regression models applicable to a wider range of socioeconomic phenomena.
Textbooks. In his first textbook (1935), Anderson tried to expound twentieth-century statistical methods using preuniversity-level mathematics. Because of the time of publication and the then predominant doctrines, its influence seems to have been stronger outside of Germany than within. His second textbook (1954), however, went through three editions in three years; it was unusual for its highly personal anecdotal style and its abundance of historical, biographical, institutional, and mathematical asides.
Students. Anderson’s best-known students, all professors in Germany, are Hans Kellerer, at Munich; Heinrich Strecker, at Tübingen; and Anderson’s son Oskar, at Mannheim. What clearly characterizes them as Andersonians, especially the former two, is a strong interest and activity in sampling-survey design, a concern for the implemental side of statistics, and avowed reservations against abstractions unrelated to practice. Strecker has also worked on variants of the variate-difference method.
Eberhard M. Fels
[For discussion of the history and subsequent development of the fields in which Anderson worked, seeNonparametric statistics; Probability; Sample surveys; Tlme series.]
WORKS BY ANDERSON
(1929a) 1949 Über die repräsentative Methode und deren Anwendung auf die Aufarbeitung der Ergebnisse der bulgarischen landwirtschaftlichen Betriebszählung vom 31. XII. 1926. Munich: Bayerisches Statistisches Landesamt. → First published in Bulgarian.
1929b Zur Problematik der empirisch-statistischen Konjunkturforschung: Kritische Betrachtung der HarvardMethoden. Bonn: Schroeder.
1931 Ist die Quantitätstheorie statistisch nachweisbar? Zeitschrift für Nationalökonomie 2:523–578.
(1934) 1959 Statistical Method. Volume 14, pages 366–371 in Encyclopaedia of the Social Sciences. New York: Macmillan.
1935 Einführung in die mathematische Statistik. Vienna: Springer.
1952 Wieder eine Indexverkettung? Mitteilungsblatt für mathematische Statistik 4:32–47.
(1954) 1962 Probleme der statistischen Methodenlehre in den Sozialwissenschaften. 4th ed. Würzburg (Germany): Physica-Verlag. … Pages cited in text refer to the 1957 edition.
1955a Eine “nicht-parametrische” (verteilungsfreie) Ableitung der Streuung (Variance) des multiplen (Rz.xy) und partiellen (Rxy.z) Korrelationskoeffizienten im Falle der sogenannten Null-hypothese, sowie der dieser Hypothese entsprechenden mittleren quadratischen Abweichungen (Standard Deviations) der Regressionskoeffizienten. Mitteilungsblatt für mathematische Statistik 7:85–112.
1955b Wann ist der Korrelationsindex von Fechner “Gesichert” (Significant)? Mitteilungsblatt für mathematische Statistik 7:166–167.
1963 Ausgewählte Schriften. 2 vols. Edited by H. Kellerer et al. Tübingen (Germany): Mohr. → Contains most of Anderson’s extant papers—translated into German if originals are in other languages—and a biography.
SUPPLEMENTARY BIBLIOGRAPHY
Karpenko, B. I. 1957 Zhizn’ i deiatel’nost’ A. A. Chuprova (The Life and Activity of A. A. Chuprov). Akademüa nauk SSSR, Otdelenie ekonomicheskikh, filosofskikh i pravovykh nauk, Uchenye zapiski po statistike 3:282–317.
Tintner, Gerhard 1940 The Variate Difference Method. Bloomington, Ind.: Principia Press.
Tintner, Gerhard 1961 The Statistical Work of Oskar Anderson. Journal of the American Statistical Association 56:273–280. → Contains a bibliography.
Volkov, A. G. 1961 Vyborochnoe nabliudenie naseleniia (The Sample Survey of Population). Akademiia nauk SSSR, Otdelenie ekonomicheskikh, filosofskikh i pravovykh nauk, Uchenye zapiski po statistike 6:157–184.
Wold, Herman 1961 Oskar Anderson: 1887–1960. Annals of Mathematical Statistics 32:651–660. → Contains a bibliography.