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Asymptotic power properties of the Cramér-von Mises test under contiguous alternatives

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  • Neuhaus, Georg

Abstract

The asymptotic power of the Cramér-von Mises test (CvM test) when parameters are estimated from the data is studied under certain local (contiguous) alternatives. The notion of (asymptotic) direction and distance from the null hypothesis of alternatives is introduced, and it is shown that there exist directions with maximum, minimum, and arbitrary intermediate power. For each direction, there exists a natural asymptotic testing problem with an uniformly most powerful test that is compared with the CvM test. For that, the notion of asymptotic local efficiency (ALE) of the CvM test is introduced. finally, the influence of more information on the (unknown) parameter is studied for three tests of the CvM-type for independence. it is shown that for certain directions, a better knowledge of the parameter may increase the power, and for other ones decrease it. These properties are analogous to that of the X2-test in similar situations.

Suggested Citation

  • Neuhaus, Georg, 1976. "Asymptotic power properties of the Cramér-von Mises test under contiguous alternatives," Journal of Multivariate Analysis, Elsevier, vol. 6(1), pages 95-110, March.
    • Handle: RePEc:eee:jmvana:v:6:y:1976:i:1:p:95-110
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    1. repec:cte:wsrepe:ws035312 is not listed on IDEAS
    2. Dencker Peter & Liese Friedrich, 2004. "Local maximin properties of tests in Gaussian shift experiments," Statistics & Risk Modeling, De Gruyter, vol. 22(2), pages 83-108, February.
    3. Dante Amengual & Marine Carrasco & Enrique Sentana, 2017. "Testing Distributional Assumptions Using a Continuum of Moments," Working Papers wp2018_1709, CEMFI.
    4. Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra.
    5. Song, Kyungchul, 2010. "Testing semiparametric conditional moment restrictions using conditional martingale transforms," Journal of Econometrics, Elsevier, vol. 154(1), pages 74-84, January.
    6. T. Fischer & U. Kamps, 2013. "Power maps in goodness-of-fit testing," Computational Statistics, Springer, vol. 28(3), pages 1365-1382, June.
    7. Rahnenführer Jörg, 2003. "On preferences of general two-sided tests with applications to Kolmogorov–Smirnov-type tests," Statistics & Risk Modeling, De Gruyter, vol. 21(2), pages 149-170, February.
    8. Glimm, Ekkehard & Läuter, Jürgen, 2003. "On the admissibility of stable spherical multivariate tests," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 254-265, August.
    9. Amengual, Dante & Carrasco, Marine & Sentana, Enrique, 2020. "Testing distributional assumptions using a continuum of moments," Journal of Econometrics, Elsevier, vol. 218(2), pages 655-689.
    10. Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September.
    11. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
    12. Juan Carlos Escanciano, 2005. "On the Asymptotic Power Properties of Specification Tests for Dynamic Parametric Regressions," Faculty Working Papers 07/05, School of Economics and Business Administration, University of Navarra.

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