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Density testing in a contaminated sample

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  • Holzmann, Hajo
  • Bissantz, Nicolai
  • Munk, Axel

Abstract

We study non-parametric tests for checking parametric hypotheses about a multivariate density f of independent identically distributed random vectors Z1,Z2,... which are observed under additional noise with density [psi]. The tests we propose are an extension of the test due to Bickel and Rosenblatt [On some global measures of the deviations of density function estimates, Ann. Statist. 1 (1973) 1071-1095] and are based on a comparison of a nonparametric deconvolution estimator and the smoothed version of a parametric fit of the density f of the variables of interest Zi. In an example the loss of efficiency is highlighted when the test is based on the convolved (but observable) density g=f*[psi] instead on the initial density of interest f.

Suggested Citation

  • Holzmann, Hajo & Bissantz, Nicolai & Munk, Axel, 2007. "Density testing in a contaminated sample," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 57-75, January.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:1:p:57-75
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    References listed on IDEAS

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    1. Neumann, Michael H. & Paparoditis, Efstathios, 2000. "On bootstrapping L2-type statistics in density testing," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 137-147, November.
    2. Politis, Dimitris N. & Romano, Joseph P., 1999. "Multivariate Density Estimation with General Flat-Top Kernels of Infinite Order," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 1-25, January.
    3. Delaigle, A. & Gijbels, I., 2004. "Practical bandwidth selection in deconvolution kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 249-267, March.
    4. P. Groeneboom & G. Jongbloed, 2003. "Density estimation in the uniform deconvolution model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(1), pages 136-157.
    5. Efstathios Paparoditis, 2000. "Spectral Density Based Goodness-of-Fit Tests for Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 143-176.
    6. A. Delaigle & I. Gijbels, 2002. "Estimation of integrated squared density derivatives from a contaminated sample," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 869-886.
    7. van Es, A. J. & Kok, A. R., 1998. "Simple kernel estimators for certain nonparametric deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 151-160, August.
    8. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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    Cited by:

    1. Meister, Alexander, 2009. "On testing for local monotonicity in deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 312-319, February.
    2. Taisuke Otsu & Luke Taylor, 2016. "Specification testing for errors-in-variables models," STICERD - Econometrics Paper Series /2015/586, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Nicolai Bissantz & Gerda Claeskens & Hajo Holzmann & Axel Munk, 2009. "Testing for lack of fit in inverse regression-with applications to biophotonic imaging," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 25-48.
    4. Zu, Yang, 2015. "Nonparametric specification tests for stochastic volatility models based on volatility density," Journal of Econometrics, Elsevier, vol. 187(1), pages 323-344.

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