Chapter 17 Goodness-of-Fit Tests
Although Fisher was fond of pointing out the difficulties of assuming the correct prior distribution p(θ), he did not disdain to make a prodigious leap of faith in his selection of f (x|θ).
– Richard A. Tapia and James R. Thompson
17.1 Introduction
In traditional exposition of inferential statistics usually the family of distributions that model the data is given or assumed. Typically, the family is generated by a single distribution known up to a parameter or vector of parameters. Then the analysis proceeds to estimate or test the parameters which results in narrowing the family to a specific distribution. Often the distribution is tacitly assumed (Poisson, binomial, normal, exponential, etc.) and the interest is only in the parameters specifying the location or spread of such distributions. All this was done in Chapters 7 through 11.
Should we be more critical? Before the model or a family of models describing data is “assumed known,” we should think how to select the model and test its adequacy.
Goodness-of-fit tests are procedures that test whether the distribution of a sample conforms to some ...
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