Impact of Karl Pearson's Work on Statistical Developments in India

Karl Pearson's work greatly inspired P. C. Mahalanobis's interest in statistics, who was at the centre of modern statistical developments in India. Mahalanobis learned statistics on his own, reading Pearson's articles and his journal, and encouraged others to study Pearson's papers. Pearson was a Honorary Fellow of the Indian Statistical Institute, which has been a leading statistical training and research center in India. The statistical revolution that Pearson brought also facilitated the training and research of many Indian statisticians.     

Karl Pearson's Influence in the United States

Karl Pearson, the founder of mathematical statistics, was the leading statistical researcher from the 1890s up to about 1920. His interests were wide-ranging and so his impact on statistics in the United States was also wide-ranging. Many American researchers came to University College London to study with him. Others studied his work from afar. In the United States, Pearsonian statistics first penetrated the academic landscape in biology. This was soon followed by the fields of economics and psychology. It was not until relatively late in Pearson's career that several American mathematicians took up statistics as a serious research topic.     

Karl Pearson—The Scientific Life in a Statistical Age by Theodore M. Porter: A Review

Porter presents an excellent account of the young Karl Pearson and his extraordinarily varied activities. These ranged from the Cambridge Mathematical Tripos Exams to German history and folklore, and included free thought, socialism, the woman's question, and the law. Returning to science, Pearson produced the famous Grammar of Science . He decided on a career in statistics only at age 35. Porter emphasizes Pearson's often acrimonious but largely successful battles to show the wide applicability and importance of statistics in many areas of science and public affairs. Eugenics became a passion for Pearson. Avoiding all formulas Porter fails to give any concrete ideas of even Pearson's most important contributions to statistical theory. We try to sketch these here.     

Karl Pearson and the Origin of Kurtosis

Although the kurtosis index proposed by Karl Pearson in 1905 is introduced in statistical textbooks at all levels, the measure is not easily interpreted and has been a subject of considerable debate. In this study, the theoretical development of kurtosis is surveyed from a historical perspective of Pearson's work on evolution. It surprisingly emerges that there was no emphasis in Pearson's papers on kurtosis as measuring (in part) tail heaviness. However, it is found that Pearson used to frequently adjust the formalisation of kurtosis depending on his changing needs. This complex development partly explains the confusion that would surround kurtosis in subsequent literature. Our conclusion is that most misunderstandings arise from improper use of the kurtosis coefficient outside the Pearson system of frequency curves.     

Karl Pearson in Russian Contexts

The confluence of statistics and probability into mathematical statistics in the Russian Empire through the interaction, 1910–1917, of A.A. Chuprov and A.A. Markov was influenced by the writings of the English Biometric School, especially those of Karl Pearson. The appearance of the Russian-language exposition of Pearsonian ideas by E. E. Slutsky in 1912 was instrumental in this confluence. Slutsky's predecessors in such writings (Lakhtin, Orzhentskii, and Leontovich) were variously of mathematical, political economy, and biological backgrounds. Work emanating from the interpolational nature of Pearson's system of frequency curves was continued subsequently through the work of Markov, Bernstein, Romanovsky, and Kravchuk (Krawtchouk), who laid a solid probabilistic foundation. The correlational nature in the interpolational early work of Chebyshev, and work of the English Biometric School in the guise of linear least-squares fitting exposited as the main component of Slutsky's book, was developed in population as well as sample context by Chuprov. He also championed the expectation operation in providing exact relations between sample and population moments, in direct interaction with Karl Pearson. Romanovsky emerges as the most adaptive and modern mathematical statistician.     

Pearson's Statistics in the Netherlands and the Astronomer Kapteyn

In 1903 the well-known Dutch astronomer Kapteyn published a paper in which he discussed statistical methods which he thought would be relevant for biologists. His motivation was the 1895 paper of Pearson on skew frequency curves. Kapteyn had concluded that the theory was open to grave objections and was not adapted to nonmathematical readers. He was then led to an independent investigation of the subject. This publication would lead to a heated dialogue between Kapteyn and Pearson, in which they accused each other of inappropriate starting points, of plagiarism and of making serious mathematical mistakes. This article evaluates these claims. In addition, Kapteyn's struggle to make his work accessible to biologists is discussed.     

Ladislaus von Bortkiewicz—Statistician,Economist and a European Intellectual

Ladislaus von Bortkiewicz (1868–1931) was a European statistician. His scientific work covered theoretical economics, stochastics, mathematical statistics and radiology; today, we would call him a cross‐disciplinary scientist. With his clear views on mathematical principles with their applications in these fields, he stood in conflict with the mainstream economic schools in Germany at the dawn of the 20th century. He had many prominent students (Gumbel, Leontief and Freudenberg among them), and he carved out the path of modern statistical thinking. He was a true European intellectual with a career path from St. Petersburg via Göttingen to Straßburg and finally the Berliner Universität, now Humboldt‐Universität zu Berlin. He is known for the precise calibration of insurance claims applying the—at that time hardly known—Poisson distribution to Prussian horse kick and child suicide data. He proposed a simple solution to the Marxian transformation problem and wrote numerous articles and books on the mathematical treatment of statistical (including radiological physical) data. In this article, we sketch his life and work and point out the prominent role that he has in today's statistical thinking.     

THE "VEREENIGING VOOR DE STATISTIEK", 1857–1892

This paper deals with the history of the nineteenth century Dutch statistical society: "Vereeniging voor de Statistiek", founded in 1857. In the second half of the nineteenth century the society flourished and had a considerable amount of members. It played a very active role for the establishment of a central official statistical bureau: "Centraal Bureau voor de Statistiek". These activities ended with success in 1892. Then the society changed its name and did no longer engage itself with statistics. Members of the statistical society thought of statistics as facts about society, mostly numerical, but not always. They hoped to discover the laws which ruled society, by means of statistics. In that way the social sciences would improve.     

A Celebration of Hayek

For much of his career, the work of the Austrian economist F. A. Hayek was neglected by all but a small band of academics. The award of the Nobel Prize in Economic Science in 1974 at last brought public recognition to a scholar whose seven decades of work is increasingly seen to offer seminal analysis which will guide the development of economics for at least as long again in the future. Norman Barry, Professor of Politics at the University of Buckingham, examines Hayek's distinguished career.     

The Statistical Education of Harold Jeffreys

The paper considers the statistical work of the physicist Harold Jeffreys. In 1933–4 Jeffreys had a controversy with R.A. Fisher, the leading statistician of the time. Prior to the encounter, Jeffreys had worked on probability as the basis for scientific inference and had used methods from the theory of errors in astronomy and seismology. He had also started to rework the theory of errors on the basis of his theory of probability. After the encounter Jeffreys produced a full-scale Bayesian treatment of statistics in the form of his Theory of Probability.     

Debating Immortality: Application of Data Envelopment Analysis to Voting for the Baseball Hall of Fame

This paper applies data envelopment analysis to voting for the Baseball Hall of Fame (HOF). The approach interprets a player's career statistics as inputs and the percentage of votes that he received for the HOF as the output. A constructed frontier based on past voting defines the maximum number of votes that a player should receive based on his statistical profile. Our results suggest that about a third of the current members of the HOF (excluding Negro League players, managers, umpires, and executives) should be replaced by more deserving players. Our conclusions, however, do not account for those aspects of a player's career (both positive and negative) not captured by statistics. Copyright © 2012 John Wiley & Sons, Ltd.     

Why Distinguish Between Statistics and Mathematical Statistics–The Case of Swedish Academia

A separation between the academic subjects statistics and mathematical statistics has existed in Sweden almost as long as there have been statistics professors. The same distinction has not been maintained in other countries. Why has it been kept for so long in Sweden, and what consequences may it have had? In May 2015, it was 100 years since Mathematical Statistics was formally established as an academic discipline at a Swedish university where Statistics had existed since the turn of the century. We give an account of the debate in Lund and elsewhere about this division during the first decades after 1900 and present two of its leading personalities. The Lund University astronomer (and mathematical statistician) C. V. L. Charlier was a leading proponent for a position in mathematical statistics at the university. Charlier's adversary in the debate was Pontus Fahlbeck, professor in political science and statistics, who reserved the word statistics for ‘statistics as a social science’. Charlier not only secured the first academic position in Sweden in mathematical statistics for his former PhD student Sven Wicksell but also demonstrated that a mathematical statistician can be influential in matters of state, finance as well as in different natural sciences. Fahlbeck saw mathematical statistics as a set of tools that sometimes could be useful in his brand of statistics. After a summary of the organisational, educational and scientific growth of the statistical sciences in Sweden that has taken place during the last 50 years, we discuss what effects the Charlier–Fahlbeck divergence might have had on this development.     

Applications of the Likelihood Theory in Finance: Modelling and Pricing

This paper discusses the connection between mathematical finance and statistical modelling which turns out to be more than a formal mathematical correspondence. We like to figure out how common results and notions in statistics and their meaning can be translated to the world of mathematical finance and vice versa. A lot of similarities can be expressed in terms of LeCam’s theory for statistical experiments which is the theory of the behaviour of likelihood processes. For positive prices the arbitrage free financial assets fit into statistical experiments. It is shown that they are given by filtered likelihood ratio processes. From the statistical point of view, martingale measures, completeness, and pricing formulas are revisited. The pricing formulas for various options are connected with the power functions of tests. For instance the Black–Scholes price of a European option is related to Neyman–Pearson tests and it has an interpretation as Bayes risk. Under contiguity the convergence of financial experiments and option prices are obtained. In particular, the approximation of Itô type price processes by discrete models and the convergence of associated option prices is studied. The result relies on the central limit theorem for statistical experiments, which is well known in statistics in connection with local asymptotic normal (LAN) families. As application certain continuous time option prices can be approximated by related discrete time pricing formulas.     

做好统计基础工作,服务科学发展

经济全球化环境下,各级政府、各界人士对统计信息的依赖程度日益突显。如何保障统计数据真实准确,是社会各方面都十分关注的问题。健全的统计制度、正确的统计方法、可靠的统计资料,是提高统计信息的可信度,提升统计工作的重要意义的保障。每位统计工作者应当以务实求真的态度对待本职工作,抓好统计基础工作,服务科学发展。     

ICT Statistics at the New Millennium—Developing Official Statistics—Measuring the Diffusion of ICT and its Impact

The paper gives a short and very rough overview of the ongoing work in the field of statistics relating to the development of information and communication technology (ICT) and its impacts on the economies and on the society as a whole. It introduces three slightly different approaches with different emphasis on describing the emergence and diffusion of ICT and the respective economic and social change. These are termed the indicators approach, the new economy approach and the intellectual capital approach. The paper also discusses the basic requirements for the establishment of a new statistical system, as well as the present obstacles and problems of this work. Finally, some remarks are presented regarding further statistical co-operation in this field.     

Statistical Approaches for Non‐parametric Frontier Models: A Guided Tour

A rich theory of production and analysis of productive efficiency has developed since the pioneering work by Tjalling C. Koopmans and Gerard Debreu. Michael J. Farrell published the first empirical study, and it appeared in a statistical journal (Journal of the Royal Statistical Society), even though the article provided no statistical theory. The literature in econometrics, management sciences, operations research and mathematical statistics has since been enriched by hundreds of papers trying to develop or implement new tools for analysing productivity and efficiency of firms. Both parametric and non‐parametric approaches have been proposed. The mathematical challenge is to derive estimators of production, cost, revenue or profit frontiers, which represent, in the case of production frontiers, the optimal loci of combinations of inputs (like labour, energy and capital) and outputs (the products or services produced by the firms). Optimality is defined in terms of various economic considerations. Then the efficiency of a particular unit is measured by its distance to the estimated frontier. The statistical problem can be viewed as the problem of estimating the support of a multivariate random variable, subject to some shape constraints, in multiple dimensions. These techniques are applied in thousands of papers in the economic and business literature. This ‘guided tour’ reviews the development of various non‐parametric approaches since the early work of Farrell. Remaining challenges and open issues in this challenging arena are also described. © 2014 The Authors. International Statistical Review © 2014 International Statistical Institute     

隅谈会计人员的职业素质

会计人员的职业素质不仅决定其职业行为、职业能力和工作质量的高低,而且直接影响其职业生涯的发展,甚至影响社会经济的进步。所以,会计人员在其职业生涯中应该不断学习,自我完善,加强专业理论水平和专业基本技能、职业道德修养、法制意识和政治素质等方面的学习提高。确保实事求是、客观公正地实施职业行为,做到知法、守法,准确、规范地做好本职工作。     

Competitive On-line Statistics

A radically new approach to statistical modelling, which combines mathematical techniques of Bayesian statistics with the philosophy of the theory of competitive on-line algorithms, has arisen over the last decade in computer science (to a large degree, under the influence of Dawid's prequential statistics). In this approach, which we call "competitive on-line statistics", it is not assumed that data are generated by some stochastic mechanism; the bounds derived for the performance of competitive on-line statistical procedures are guaranteed to hold (and not just hold with high probability or on the average). This paper reviews some results in this area; the new material in it includes the proofs for the performance of the Aggregating Algorithm in the problem of linear regression with square loss.     

George Raymond Geiger (1903-1998): A Rich Life

ABSTRACT George R. Geiger, professor of Philosophy at Antioch College for fifty years, died March 19, 1998. He was a founding member of the editorial council of the American Journal of Economics and Sociology (1941-1998) and of the Antioch Review (1941-1998). He was also an advisor to and consulting editor of the Humanist (1955–59). He was the son of the founder of the Henry George School of Social Science of New York City and John Dewey's last doctoral student at Columbia University. Early on in his career he took up his father's cause, that of land value taxation; later he took up a defense of the contributions of his mentor, Dewey, and became in his own words a "journalist of philosophy."