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Chi-squared goodness of fit tests with applications / V. Voinov, M. Nikulin, N. Balakrishnan.

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Author/Creator:
Voinov, Vassiliy.
Language:
English.
Publication date:
2013
Copyright date:
2013
Imprint:
First edition.
Publication:
Amsterdam : Academic Press/Elsevier, [2013]
Copyright notice:
©2013
Format:
  • Book
  • xii, 229 pages : illustrations ; 24 cm
Bibliography:
Includes bibliographical references (p. 215-226) and index.
Summary:
"If the number of sample observations n ! 1, the statistic in (1.1) will follow the chi-squared probability distribution with r-1 degrees of freedom. We know that this remarkable result is true only for a simple null hypothesis when a hypothetical distribution is specified uniquely (i.e., the parameter is considered to be known). Until 1934, Pearson believed that the limiting distribution of the statistic in (1.1) will be the same if the unknown parameters of the null hypothesis are replaced by their estimates based on a sample; see, for example, Baird (1983), Plackett (1983, p. 63), Lindley (1996), Rao (2002), and Stigler (2008, p. 266). In this regard, it is important to reproduce the words of Plackett (1983, p. 69) concerning E. S. Pearson's opinion: "I knew long ago that KP (meaning Karl Pearson) used the 'correct' degrees of freedom for (a) difference between two samples and (b) multiple contingency tables. But he could not see that in curve fitting should be got asymptotically into the same category." Plackett explained that this crucial mistake of Pearson arose from to Karl Pearson's assumption "that individual normality implies joint normality." Stigler (2008) noted that this error of Pearson "has left a positive and lasting negative impression upon the statistical world." Fisher (1924) clearly showed 1 2 CHAPTER 1. A HISTORICAL ACCOUNT that the number of degrees of freedom of Pearson's test must be reduced by the number of parameters estimated from the sample"-- Provided by publisher.
Contributor:
Balakrishnan, N., 1956-
Nikulin, M. S. (Mikhail Stepanovich)
Subjects:
ISBN:
9780123971944
0123971942

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