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Cramér-von Mises statistics based on the sample quantile function and estimated parameters

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  • LaRiccia, Vincent
  • Mason, David M.

Abstract

The estimated weighted empirical quantile process is introduced, and under mild regularity conditions is shown to converge weakly in L2(0, 1) to a Gaussian process. This leads to an elementary approach to the derivation of the asymptotic null distribution of Cramér-von Mises type statistics for testing a composite null hypothesis based on the sample quantile function and estimated parameters. Special emphasis is given to the location/scale composite null hypothesis.

Suggested Citation

  • LaRiccia, Vincent & Mason, David M., 1986. "Cramér-von Mises statistics based on the sample quantile function and estimated parameters," Journal of Multivariate Analysis, Elsevier, vol. 18(1), pages 93-106, February.
    • Handle: RePEc:eee:jmvana:v:18:y:1986:i:1:p:93-106
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    Cited by:

    1. Beirlant, J. & Mason, D. M. & Vynckier, C., 1999. "Goodness-of-fit analysis for multivariate normality based on generalized quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 119-142, April.
    2. Koji Tsukuda, 2017. "A change detection procedure for an ergodic diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 833-864, August.

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