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Journal of Statistical Theory and Practice

, Volume 3, Issue 3, pp 705–733 | Cite as

Informative Statistical Analyses Using Smooth Goodness of Fit Tests

  • O. ThasEmail author
  • J. C. W. Rayner
  • D. J. Best
  • B. De Boeck
Article

Abstract

We propose a methodology for informative goodness of fit testing that combines the merits of both hypothesis testing and nonparametric density estimation. In particular, we construct a data-driven smooth test that selects the model using a weighted integrated squared error (WISE) loss function. When the null hypothesis is rejected, we suggest plotting the estimate of the selected model. This estimate is optimal in the sense that it minimises the WISE loss function. This procedure may be particularly helpful when the components of the smooth test are not diagnostic for detecting moment deviations. Although this approach relies mostly on existing theory of (generalised) smooth tests and nonparametric density estimation, there are a few issues that need to be resolved so as to make the procedure applicable to a large class of distributions. In particular, we will need an estimator of the variance of the smooth test components that is consistent in a large class of distributions for which the nuisance parameters are estimated by method of moments. This estimator may also be used to construct diagnostic component tests.

The properties of the new variance estimator, the new diagnostic components and the proposed informative testing procedure are evaluated in several simulation studies. We demonstrate the new methods on testing for the logistic and extreme value distributions.

Key-words

Generalised score test Method of moment estimator Nonparametric density estimation Orthonormal polynomials 

AMS Subject Classification

62G07 62G10 

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Copyright information

© Grace Scientific Publishing 2009

Authors and Affiliations

  • O. Thas
    • 1
    Email author
  • J. C. W. Rayner
    • 2
  • D. J. Best
    • 2
  • B. De Boeck
    • 1
  1. 1.Department of Applied Mathematics, Biometrics and Process ControlGhent UniversityGentBelgium
  2. 2.School of Mathematical and Physical SciencesUniversity of NewcastleAustralia

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