Harald Höffding.

Jan, Patočka

doi:10.1037/11082-008

Cited by 10 publications

(9 citation statements)

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“…For question (C), the answer is more involved, because ρ R,G is determined by the joint distribution of {R J , G J } induced by the uniform distribution over J , but D O and D U are characteristics of the marginal distributions of R J and of G J , respectively. Although marginal means and variances (e.g., f, σ 2 G ) are not often perceived to affect correlations (e.g., ρ R,G ), in general they do impose restrictions because of the Hoeffding identity [Höffding (1940)]…”

Section: A Fundamental Identity For Data Quality-quantity Tradeoffmentioning

confidence: 99%

Statistical paradises and paradoxes in big data (I): Law of large populations, big data paradox, and the 2016 US presidential election

Meng¹

2018

Ann. Appl. Stat.

219

233

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Statisticians are increasingly posed with thought-provoking and even paradoxical questions, challenging our qualifications for entering the statistical paradises created by Big Data. By developing measures for data quality, this article suggests a framework to address such a question: "Which one should I trust more: a 1% survey with 60% response rate or a self-reported administrative dataset covering 80% of the population?" A 5-element Eulerformula-like identity shows that for any dataset of size n, probabilistic or not, the difference between the sample average X n and the population average X N is the product of three terms: (1) a data quality measure, ρ R,X , the correlation between X j and the response/recording indicator R j ; (2) a data quantity measure, √ (N − n)/n, where N is the population size; and (3) a problem difficulty measure, σ X , the standard deviation of X. This decomposition provides multiple insights: (I) Probabilistic sampling ensures high data quality by controlling ρ R,X at the level of N −1/2 ; (II) When we lose this control, the impact of N is no longer canceled by ρ R,X , leading to a Law of Large Populations (LLP), that is, our estimation error, relative to the benchmarking rate 1/ √ n, increases with √ N; and (III) the "bigness" of such Big Data (for population inferences) should be measured by the relative size f = n/N , not the absolute size n; (IV) When combining data sources for population inferences, those relatively tiny but higher quality ones should be given far more weights than suggested by their sizes.Estimates obtained from the Cooperative Congressional Election Study (CCES) of the 2016 US presidential election suggest a ρ R,X ≈ −0.005 for self-reporting to vote for Donald Trump. Because of LLP, this seemingly minuscule data defect correlation implies that the simple sample proportion of the self-reported voting preference for Trump from 1% of the US eligible voters, that is, n ≈ 2,300,000, has the same mean squared error as the corresponding sample proportion from a genuine simple random sample of size n ≈ 400, a 99.98% reduction of sample size (and hence our confidence). The

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Section: A Fundamental Identity For Data Quality-quantity Tradeoffmentioning

confidence: 99%

Statistical paradises and paradoxes in big data (I): Law of large populations, big data paradox, and the 2016 US presidential election

Meng¹

2018

Ann. Appl. Stat.

219

233

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“…Edgar Rubin participated in the Ninth International Congress of Psychology at Yale, presenting two papers (Rubin, 1930a, 1930b). A few days after the congress, Rubin wrote to Høffding, telling him of the decision to hold the Tenth Congress in Copenhagen and that James McKeen Cattell, the president of the Yale Congress, had stated, when proposing Copenhagen as the venue of the next meeting, that it “was a tribute to you and on the whole an acknowledgment of the psychological work that has been carried out in Denmark” (Høffding, 1843–1931, Rubin to Høffding, September 12, [1929]) 1…”

Section: Building Up To the Congressmentioning

confidence: 99%

Before the deluge: The 1932 International Congress of Psychology in Copenhagen.

Pind

2019

History of Psychology

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The Tenth International Congress of Psychology, held in Copenhagen in late August of 1932, was the last International Congress held before events leading up to World War II came to interfere with the course of the congresses. Despite the difficult times, primarily because of the Great Depression and the fragile political situation, the congress nevertheless managed to bring together participants from many countries, thus emphasizing the international profile of psychology. The 1932 congress was characterized by the wide range of topics presented and discussed. A book of proceedings, containing all the papers delivered, was planned but never appeared, as the organizers of the congress were unable to obtain funds required for the publication. Therefore, relatively little has been written about the congress. The congress, however, aroused great interest in the Danish newspapers. Many participants took part in interviews, casting an interesting light on their approaches to psychology. The newspaper reports, along with archival sources, make it possible to describe the course of the conference. It clearly emerges that psychology had, by this time, shed the narrow experimental focus of its earliest decades. The gathering clouds of international unrest had some effects on the course of the congress. Shortly after the congress, the careers and even the lives of many of the participants faced serious challenges. (PsycINFO Database Record

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“…The identity (2.1) can be found in Shorack [2000], section 7.4, formula page 117, but it has its origins in Höffding [1940] (see also Hoeffding [1994] for a translation of the German original) This identity has several useful corollaries. We begin with the original inequality due to Höffding [1940], by taking a and b to be identity functions.…”

Section: Covariance Identitiesmentioning

confidence: 99%