Abstract
Suppose a smooth test of goodness of fit has been applied to assess the validity of a parametric analysis, such as an analysis of variance. If the smooth test rejects the distributional assumption, the original parametric model can be replaced by the order k smooth alternative that is the basis of the smooth test. Here we demonstrate that basing the analysis on such an alternative, when it is consistent with the data, may result not only in a valid analysis, but also in a test with greater power than for the original parametric analysis. Several examples are given, including the one sample t-test, the one-way analysis of variance and randomised complete block designs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramowitz, M., Stegun, I.A., 1972. Handbook of Mathematical Functions. Dover, New York.
Carolan, A.M., 2000. Partially Parametric Testing. Unpublished PhD thesis. School of Mathematics and Applied Statistics, University of Wollongong.
Carolan, A.M., Rayner, J.C.W., 2000a. One sample tests of location for nonnormal symmetric data. Com-mun. Statist.-Theor. Meth., 29(7), 1569–1581.
Carolan, A.M., Rayner, J.C.W., 2000b. Wald tests of location for symmetric nonnormal data. Biometrical Journal, 42(6), 777–792.
Carolan, A.M., Rayner, J.C.W., 2001. One sample tests for the location of modes of nonnormal data. Journal of Applied Mathematics and Decision Sciences, 5(1), 1–19.
Frets, G.P. (1921), Heredity of head form in man. Genetica, 3, 193–384.
Hand, D.J., Daly, F., Lunn, A.D., McConway, K.J., Ostrowski, E., 1994. A Handbook of Small Data Sets. Chapman and Hall, London.
Manly, B.F.J., 1986. Multivariate Statistical Methods. Chapman and Hall, New York.
Rayner, J.C.W., 1997. The Asymptotically Optimal Tests. J.R.S.S., Series D (The Statistician), 46(3), 337–346.
Rayner, J.C.W., 2001. Partially parametric testing. Chapter 32 in Goodness-of-Fit Tests and Validity of Models, Huber-Carol, C., Balakrishnan, N., Nikulin, M. S., Mesbah, M. (editors), Birkhauser, Boston, 423-431.
Rayner, J.C.W., Best, D.J., 1989. Smooth Tests of Goodness of Fit. Oxford University Press, New York.
Rayner, J.C.W., Best, D.J., Thas, O., 2009a. Generalised smooth tests of goodness of fit. Journal of Statistical Theory and Practice, 3(3), 665–679. Companion paper.
Rayner, J.C.W., Thas, O., Best, D.J., 2009b. Smooth Tests of Goodness of Fit: Using R (2nd ed.). Wiley, Singapore.
Sokal, R.R., Rohlf, F.J., 1995. Biometry: the Principals and Practice of Statistics in Biological Research. Freeman, New York.
Thomson, A., Randall-MacIver, R., 1905. Ancient Races of the Thebaid. Oxford University Press, Oxford.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rayner, J.C.W., Carolan, A.M. Partially Parametric Testing. J Stat Theory Pract 3, 735–750 (2009). https://doi.org/10.1080/15598608.2009.10411956
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1080/15598608.2009.10411956