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A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935A Nonprobabilistic Interlude: The Fitting of Equations to Data, 1750–1805

A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935: A... [We consider the model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ y_i = f\left( {x_{i1} ,...,x_{im} ;\beta _1 ,...,\beta _m } \right) + \varepsilon _i ,i = 1,...,n,m \leqslant n, $$\end{document} , where the ys represent the observations of a phenomenon, whose variation depends on the observed values of the xs, the βs are unknown parameters, and the εs random errors, distributed symmetrically about zero. Denoting the true value of y by η, the model may be described as a mathematical law giving the dependent variable η as a function of the independent variables x1, ..., xm with unknown errors of observation equal to ε = y − η.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935A Nonprobabilistic Interlude: The Fitting of Equations to Data, 1750–1805

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Publisher
Springer New York
Copyright
© Springer Science+Business Media, LLC 2007
ISBN
978-0-387-46408-4
Pages
47 –53
DOI
10.1007/978-0-387-46409-1_6
Publisher site
See Chapter on Publisher Site

Abstract

[We consider the model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ y_i = f\left( {x_{i1} ,...,x_{im} ;\beta _1 ,...,\beta _m } \right) + \varepsilon _i ,i = 1,...,n,m \leqslant n, $$\end{document} , where the ys represent the observations of a phenomenon, whose variation depends on the observed values of the xs, the βs are unknown parameters, and the εs random errors, distributed symmetrically about zero. Denoting the true value of y by η, the model may be described as a mathematical law giving the dependent variable η as a function of the independent variables x1, ..., xm with unknown errors of observation equal to ε = y − η.]

Published: Jan 1, 2007

Keywords: Measurement Error Model; Unknown Error; Inconsistent Equation; Spherical Trigonometry; Extreme Error

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