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Smooth Goodness of Fit Tests

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A Parametric Approach to Nonparametric Statistics

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Abstract

Goodness of fit problems have had a long history dating back to Pearson (1900). Such problems are concerned with testing whether or not a set of observed data emanate from a specified distribution. For example, suppose we would like to test the hypothesis that a set of n observations come from a standard normal distribution.

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References

  • Adkins, L. and Fligner, M. (1998). A non-iterative procedure for maximum likelihood estimation of the parameters of Mallows’ model based on partial rankings. Communications in Statistics: Theory and Methods, 27(9):2199–2220.

    Article  MathSciNet  Google Scholar 

  • Alvo, M. and Cabilio, P. (2000). Calculation of hypergeometric probabilities using Chebyshev polynomials. The American Statistician, 54:141–144.

    Google Scholar 

  • Alvo, M. and Yu, P. L. H. (2014). Statistical Methods for Ranking Data. Springer.

    Book  Google Scholar 

  • Asmussen, S., Jensen, J., and Rojas-Nandayapa, L. (2016). Exponential family techniques for the lognormal left tail. Scandinavian Journal of Statistics, 43:774–787.

    Article  MathSciNet  Google Scholar 

  • Beckett, L. A. (1993). Maximum likelihood estimation in Mallows’ model using partially ranked data. In Fligner, M. A. and Verducci, J. S., editors, Probability Models and Statistical Analyses for Ranking Data, pages 92–108. Springer-Verlag.

    Google Scholar 

  • Busse, L. M., Orbanz, P., and Buhmann, J. M. (2007). Cluster analysis of heterogeneous rank data. In Proceedings of the 24th International Conference on Machine Learning, pages 113–120.

    Google Scholar 

  • Critchlow, D. (1985). Metric Methods for Analyzing Partially Ranked Data. Springer-Verlag: New York.

    Book  Google Scholar 

  • Critchlow, D. and Verducci, J. (1992). Detecting a trend in paired rankings. Applied Statistics, 41:17–29.

    Article  Google Scholar 

  • Critchlow, D. E., Fligner, M. A., and Verducci, J. S. (1991). Probability models on rankings. Journal of Mathematical Psychology, 35:294–318.

    Article  MathSciNet  Google Scholar 

  • Diaconis, P. (1988a). Group Representations in Probability and Statistics. Institute of Mathematical Statistics, Hayward.

    Google Scholar 

  • Efron, B. (1981). Nonparametric standard errors and confidence intervals. The Canadian Journal of Statistics, 9(2):139–158.

    Article  MathSciNet  Google Scholar 

  • Feigin, P. D. (1993). Modelling and analysing paired ranking data. In Fligner, M. A. and Verducci, J. S., editors, Probability Models and Statistical Analyses for Ranking Data, pages 75–91. Springer-Verlag.

    Google Scholar 

  • Feller, W. (1968). An Introduction to Probability Theory and Its Applications, volume I. John Wiley & Sons, Inc, New York, third edition.

    Google Scholar 

  • Fligner, M. A. and Verducci, J. S. (1986). Distance based ranking models. Journal of the Royal Statistical Society Series B, 48(3):359–369.

    MathSciNet  MATH  Google Scholar 

  • Kendall, M. and Stuart, A. (1979). The Advanced Theory of Statistics, volume 2. Griffin, London, fourth edition.

    Google Scholar 

  • Lancaster, H. (1953). A reconciliation of chi square from metrical and enumerative aspects. Sankhya, 13:1–10.

    MathSciNet  MATH  Google Scholar 

  • Lee, P. H. and Yu, P. L. H. (2012). Mixtures of weighted distance-based models for ranking data with applications in political studies. Computational Statistics and Data Analysis, 56:2486–2500.

    Article  MathSciNet  Google Scholar 

  • Mallows, C. L. (1957). Non-null ranking models. I. Biometrika, 44:114–130.

    Article  MathSciNet  Google Scholar 

  • Marden, J. I. (1995). Analyzing and Modeling Rank Data. Chapman Hall, New York.

    MATH  Google Scholar 

  • Neyman, J. (1937). Smooth test for goodness of fit. Skandinavisk Aktuarietidskrift, 20:149–199.

    MATH  Google Scholar 

  • Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine, pages 157–175.

    Article  Google Scholar 

  • Qian, Z. and Yu, P. L. H. (2018). Weighted distance-based models for ranking data using the r package rankdist. Journal of Statistical Software, page Forthcoming.

    Google Scholar 

  • Ralston, A. (1965). A First Course in Numerical Analysis. McGraw Hill, New York.

    MATH  Google Scholar 

  • Rayner, J. C. W., Best, D. J., and Thas, O. (2009a). Generalised smooth tests of goodness of fit. Journal of Statistical Theory and Practice, pages 665–679.

    Article  MathSciNet  Google Scholar 

  • Rayner, J. C. W., Thas, O., and Best, D. J. (2009b). Smooth Tests of Goodness of Fit Using R. John Wiley and Sons, 2nd edition.

    Google Scholar 

  • Serfling, Robert, J. (2009). Approximating Theorems of Mathematical Statistics. John Wiley and Sons.

    Google Scholar 

  • Siegmund, D. (1976). Importance sampling in the Monte Carlo study of sequential tests. The Annals of Statistics, 4(4):673–684.

    Article  MathSciNet  Google Scholar 

  • Yu, P. L. H. and Xu, H. (2018). Rank aggregation using latent-scale distance-based models. Statistics and Computing, page Forthcoming.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada

    Mayer Alvo

  2. Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, China

    Philip L. H. Yu

Authors
  1. Mayer Alvo
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  2. Philip L. H. Yu
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Alvo, M., Yu, P.L.H. (2018). Smooth Goodness of Fit Tests. In: A Parametric Approach to Nonparametric Statistics. Springer Series in the Data Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-94153-0_4

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