Generalised Smooth Tests of Goodness of Fit
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Smooth tests of goodness of fit may be constructed by defining an order k alternative to the hypothesised probability density function and deriving the score test to assess whether or not the data are consistent with the hypothesised probability density function. For many important distributions the form of the score test statistic is the sum of squares of components that are asymptotically independent and asymptotically standard normal. Moreover each component has a moment interpretation that assists with interpreting rejection of the null hypothesis. Here a sufficient condition is given for the score test statistic to have this form and for the components to have this simple and convenient moment interpretation. Alternative approaches, using generalised score tests, are given for when the sufficient condition is not satisfied. This enables the construction of convenient tests of fit for distributions not from exponential families of distributions, such as the logistic and extreme value distributions.
Key-wordsOrder k alternative Extreme value distribution Logistic distribution M-estimation Score and generalised score tests
AMS Subject Classification62F03 62G07 62G10
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- Bain, L., Easterman, J., Engelhardt, M., 1973. A study of life-testing models and statistical analyses for the logistic distribution. Technical Report ARL-73-0009, Aerospace Research laboratories, Wright Patterson AFB.Google Scholar
- Boos, D., 1992. On generalised score tests. The American Statistician, 47, 327–333.Google Scholar
- Coles, S., 2004. An Introduction to Statistical Modelling of Extreme Values. Springer, New York.Google Scholar