Smooth Tests of Goodness of Fit

ISBN: 9780195056105 出版年：1989 页码：177 Rayner, J C W Best, D J Oxford University Press

Summary A comprehensive approach to goodness of fit testing is possible using the smooth tests described in detail in Rayner & Best (1989). Here we give an overview of this area and demonstrate the power and flexibility of the smooth tests. Our emphasis is on the use of orthonormal functions, tests for composite hypotheses, and tests of categorised data. We have developed tests for families of distributions, such as the univariate and multivariate normal, exponential and Poisson. The tests are essentially omnibus tests but the components provide useful and powerful directional tests. The history of the smooth tests of goodness of fit is reviewed from Neyman (1937), through to Lancaster, to Thomas, Kopecky and Pierce, and to Rayner and Best. The formulation of categorised smooth models leads to X2 tests and their components. A generalisation of the smooth categorised model, when allied with Hall's (1985) idea of overlapping, leads to focused tests, and to an alternative to pooling. Examples are taken from D'Agostino & Stephens (1986), who have several different contributors and therefore approaches, none of which is recommended above the others. Our resolution is simple: don't use those other methods-use a smooth test!