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Constancy of distributions: nonparametric monitoring of probability distributions over time

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  • Hjort, N.L.
  • Koning, A.J.

Abstract

In this paper we study stochastic processes which enable monitoring the possible changes of probability distributions over time. These processes may in particular be used to test the null hypothesis of no change. The monitoring processes are bivariate functions, of time and position at the measurement scale, and are approximated with zero mean Gaussian processes under the constancy hypothesis. One may then form Kolmogorov--Smirnov or other type of tests as functionals of the processes. To study null distributions of the resulting tests, we employ KMT-type inequalities to derive Cram\\'er-type deviation results for (bootstrapped versions of) such tests statistics.

Suggested Citation

  • 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.
    • Handle: RePEc:ems:eureir:590
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    References listed on IDEAS

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    1. Samorodnitsky, Gennady, 1991. "Probability tails of Gaussian extrema," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 55-84, June.
    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. 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.
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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. 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. 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.

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