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New PDF release: A History of Parametric Statistical Inference from Bernoulli

By Anders Hald

ISBN-10: 0387464085

ISBN-13: 9780387464084

ISBN-10: 0387464093

ISBN-13: 9780387464091

This is a background of parametric statistical inference, written by way of essentially the most very important historians of information of the 20 th century, Anders Hald. This booklet may be seen as a follow-up to his newest books, even supposing this present textual content is far extra streamlined and comprises new research of many rules and advancements. and in contrast to his different books, that have been encyclopedic through nature, this publication can be utilized for a path at the subject, the one necessities being a easy direction in likelihood and statistics.

The ebook is split into 5 major sections:

* Binomial statistical inference;

* Statistical inference by way of inverse probability;

* The important restrict theorem and linear minimal variance estimation via Laplace and Gauss;

* errors thought, skew distributions, correlation, sampling distributions;

* The Fisherian Revolution, 1912-1935.

Throughout all the chapters, the writer presents vigorous biographical sketches of the various major characters, together with Laplace, Gauss, Edgeworth, Fisher, and Karl Pearson. He additionally examines the jobs performed through DeMoivre, James Bernoulli, and Lagrange, and he presents an available exposition of the paintings of R.A. Fisher.

This publication may be of curiosity to statisticians, mathematicians, undergraduate and graduate scholars, and historians of science.

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Additional info for A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935

Sample text

We call the model linear if f is linear in the s. If f is nonlinear, it is linearized by introducing approximate values of the s and using Taylor’s formula. In the following discussion of the estimation problem it is assumed that linearization has taken place so that the reduced model becomes yi =  1 xi1 + · · · +  m xim + %i , i = 1, . . , n, m  n. 1) For one independent variable we often use the form yi =  + xi + %i . 1) is written as y = X + %. In the period considered no attempts were made to study the sampling distribution of the estimates.

In a discussion of the figure of the Earth, Laplace [153] proves Boscovich’s result simply by dierentiation of S(b). 4). In the Mécanique Céleste, ([154] Vol. 2) Laplace returns to the problem and proposes to use Boscovich’s two conditions directly on the measurements of the arcs instead of the arc lengths per degree; that is, instead S of yi he considers of degrees. Hence, he minimizes wi |yi abxi | wi yi , where wi is the number S under the restriction wi (yi  a  bxi ) = 0. 4) by substituting wi |Xi | for |Xi |.

1 The Measurement Error Model We consider the model yi = f (xi1 , . . , xim ;  1 , . . ,  m ) + %i , i = 1, . . , n, m  n, where the ys represent the observations of a phenomenon, whose variation depends on the observed values of the xs, the s are unknown parameters, and the %s random errors, distributed symmetrically about zero. Denoting the true value of y by , the model may be described as a mathematical law giving the dependent variable  as a function of the independent variables x1 , .

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A History of Parametric Statistical Inference from Bernoulli to Fisher, 1713–1935 by Anders Hald

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