Studies in the History of Probability and Statistics. XXIX: The Discovery of the Method of Least Squares

Plackett, R. L.

doi:10.2307/2334569

Cited by 47 publications

(27 citation statements)

References 4 publications

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“…( [3], p. 258) It shall not go unmentioned that in his 'Theoria motus' Gauss also claimed the discovery of the method of least squares, thereby enraging Legendre who had published said method four years earlier and claimed priority, eventually inciting -to put it in the words of Stigler ([4], p. 465) -"the most famous priority dispute in the history of statistics". It appears that Gauss had indeed discovered the method well before Legendre but failed to share the discovery with the broad community at the time [4][5][6][7].…”

Section: Historical Background Of the Normal Distributionmentioning

confidence: 99%

“…The former, as the term implies, requires a contractual relationship between the parties 4 while the latter covers faulty conduct ('Verschuldenshaftung') as well as strict (as for there is no fault requirement) liability ('Gefährdungshaftung') 5 . They will be addressed in the above order.…”

Section: Contractual Liabilitymentioning

confidence: 99%

“…The law of negotiorum gestio ('Geschäftsführung ohne Auftrag') follows in § 677 BGB while unjustified enrichment ('ungerechtfertigte Bereicherung') is regulated by § § 812 ff. BGB" [46], p. 24 5 "The BGB devotes thirty paragraphs (not including § 835 BGB which was repealed) to the law of torts -and they form the twenty-fifth title of the second book dealing with obligations. The term unerlaubte Handlungen is often used to cover the domain that Anglo-American lawyers would ascribe to 'torts' but the term used precisely is best understood to cover faulty conduct (Verschuldenshaftung).…”

Section: Requirementsmentioning

confidence: 99%

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Defensive Signal Processing: The Case for the Use of Nonparametric and Robust Statistical Methods to Reduce Product Liability Exposure

Lang¹

2017

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This paper makes the case that in an Internet of Things (IoT) world where data processing has become pervasive, the assessment of whether or not the underlying (statistical) modeling assumptions are justified and appropriate should no longer be limited to the perspective of mathematical statistics alone. The paper argues that large parts of sound academic research in engineering lack practical merit in that, akin to a concept car, they are not market-ready, most commonly due to feasibility and liability issues. Through an analysis of both statistical and legal aspects it will be shown that the stoic pursuit of 'optimality' more often than not yields to risky and suboptimal outcomes when applied to actual physical world problems. To address this, the concept of 'Defensive Signal Processing' is introduced and future research directions are briefly outlined.

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Section: Historical Background Of the Normal Distributionmentioning

confidence: 99%

Section: Contractual Liabilitymentioning

confidence: 99%

Section: Requirementsmentioning

confidence: 99%

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Defensive Signal Processing: The Case for the Use of Nonparametric and Robust Statistical Methods to Reduce Product Liability Exposure

Lang¹

2017

Preprint

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“…A detailed history of the field from these early 1 The discovery of the method of least squares, one of the key algorithms in system identification by Adrien-Marie Legendre and Carl Friedrich Gauss lead to one of the more famous priority disputes in the history of statistics. An interesting documentation of this rather public quarrel was written by Plackett [138].…”

Section: Contentsmentioning

confidence: 99%

Graphical model driven methods in adaptive system identification

Yellepeddi¹

2016

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Identifying and tracking an unknown linear system from observations of its inputs and outputs is a problem at the heart of many different applications. Due to the complexity and rapid variability of modern systems, there is extensive interest in solving the problem with as little data and computation as possible.This thesis introduces the novel approach of reducing problem dimension by exploiting statistical structure on the input. By modeling the input to the system of interest as a graph-structured random process, it is shown that a large parameter identification problem can be reduced into several smaller pieces, making the overall problem considerably simpler.Algorithms that can leverage this property in order to either improve the performance or reduce the computational complexity of the estimation problem are developed. The first of these, termed the graphical expectation-maximization least squares (GEM-LS) algorithm, can utilize the reduced dimensional problems induced by the structure to improve the accuracy of the system identification problem in the low sample regime over conventional methods for linear learning with limited data, including regularized least squares methods.Next, a relaxation of the GEM-LS algorithm termed the relaxed approximate graph structured least squares (RAGS-LS) algorithm is obtained that exploits structure to perform highly efficient estimation. The RAGS-LS algorithm is then recast into a recursive framework termed the relaxed approximate graph structured recursive least squares (RAGS-RLS) algorithm, which can be used to track time-varying linear systems with low complexity while achieving tracking performance comparable to much more computationally intensive methods.The performance of the algorithms developed in the thesis in applications such as channel identification, echo cancellation and adaptive equalization demonstrate that the gains admitted by the graph framework are realizable in practice. The methods have wide applicability, and in particular show promise as the estimation and adaptation algorithms for a new breed of fast, accurate underwater acoustic modems.The contributions of the thesis illustrate the power of graphical model structure in simplifying difficult learning problems, even when the target system is not directly structured.Thesis Supervisor: James C. Preisig Title: Scientist Emeritus, Woods Hole Oceanographic Institution AcknowledgmentsPiglet noticed that even though he had a Very Small Heart, it could hold a rather large amount of Gratitude. Winnie the PoohA.A.MilneMy years at MIT have been about so much more than a degree. In the past six years you have introduced to more worlds than I ever knew existed. As this long and wonderful journey ends, I find that my heart can, too, hold so much gratitude, for everything that you have given.Of course, I haven't said who "you" is, so here goes.It is impossible to write any list of acknowledgements without having at the very top my thesis advisor Dr. James Preisig, who has truly been a wide-angle lens f...

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“…[Plackett (1972) has an intriguing discussion of their relative rights to priority.] As noted by Scheffe (1956), an interesting aspect of those two early nineteenth century papers is that they both appear in books on astronomy.…”

Section: The Early Yearsmentioning

confidence: 99%