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Constancy of distributions: asymptotic efficiency of certain nonparametric tests of constancy

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  • Koning, A.J.
  • Hjort, N.L.

Abstract

In this paper we study stochastic processes which enable monitoring the possible changes of probability distributions over time. These so-called monitoring processes are bivariate functions of time and position at the measurement scale, and in particular be used to test the null hypothesis of no change: one may then form Kolmogorov--Smirnov or other type of tests as functionals of the processes. In Hjort and Koning (2001) Cram??r-type deviation results were obtained under the constancy null hypothesis for [bootstrapped versions of] such ``derived'' test statistics. Here the behaviour of derived test statistics is investigated under alternatives in the vicinity of the constancy hypothesis. When combined with Cram??r-type deviation results, the results in this paper enable the computation of efficiencies of the corresponding tests. The discussion of some examples of yield guidelines for the choice of the test statistic, and hence for the underlying monitoring process.

Suggested Citation

  • Koning, A.J. & Hjort, N.L., 2002. "Constancy of distributions: asymptotic efficiency of certain nonparametric tests of constancy," Econometric Institute Research Papers EI 2002-33, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:548
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    File URL: https://repub.eur.nl/pub/548/feweco20020920122925.pdf
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    References listed on IDEAS

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    1. Hjort, N.L. & Koning, A.J., 2001. "Constancy of distributions: nonparametric monitoring of probability distributions over time," Econometric Institute Research Papers EI 2001-50, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Koning, A.J. & Protassov, V., 2001. "Tail behaviour of Gaussian processes with applications to the Brownian pillow," Econometric Institute Research Papers EI 2001-49, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Kallenberg, Wilbert C. M. & Koning, Alex J., 1995. "On Wieand's theorem," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 121-132, November.
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    Cited by:

    1. Koning, A.J. & Franses, Ph.H.B.F., 2003. "Did the incidence of high precipitation levels increase? Statistical evidence for the Netherlands," Econometric Institute Research Papers EI 2003-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Hjort, N.L. & Koning, A.J., 2001. "Constancy of distributions: nonparametric monitoring of probability distributions over time," Econometric Institute Research Papers EI 2001-50, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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    2. Koning, A.J. & Franses, Ph.H.B.F., 2003. "Did the incidence of high precipitation levels increase? Statistical evidence for the Netherlands," Econometric Institute Research Papers EI 2003-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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