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Correction of Density Estimators that are not Densities

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  • Ingrid K. Glad

Abstract

Several old and new density estimators may have good theoretical performance, but are hampered by not being bona fide densities; they may be negative in certain regions or may not integrate to 1. One can therefore not simulate from them, for example. This paper develops general modification methods that turn any density estimator into one which is a bona fide density, and which is always better in performance under one set of conditions and arbitrarily close in performance under a complementary set of conditions. This improvement-for-free procedure can, in particular, be applied for higher-order kernel estimators, classes of modern "h"-super-4 bias kernel type estimators, superkernel estimators, the sinc kernel estimator, the "k"-NN estimator, orthogonal expansion estimators, and for various recently developed semi-parametric density estimators. Copyright Board of the Foundation of the Scandinavian Journal of Statistics 2003..

Suggested Citation

  • Ingrid K. Glad, 2003. "Correction of Density Estimators that are not Densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 415-427.
  • Handle: RePEc:bla:scjsta:v:30:y:2003:i:2:p:415-427
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    References listed on IDEAS

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    1. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, pages 31-48.
    2. Zonghui Hu & Dean A. Follmann & Jing Qin, 2010. "Semiparametric dimension reduction estimation for mean response with missing data," Biometrika, Biometrika Trust, vol. 97(2), pages 305-319.
    3. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, pages 1221-1246.
    4. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    5. Ding, Xiaobo & Wang, Qihua, 2011. "Fusion-Refinement Procedure for Dimension Reduction With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1193-1207.
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    Cited by:

    1. Olivier Thas, 2009. "Comments on: Goodness-of-fit tests in mixed modes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, pages 260-264.
    2. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, pages 99-110.
    3. Chacón, José E. & Monfort, Pablo & Tenreiro, Carlos, 2014. "Fourier methods for smooth distribution function estimation," Statistics & Probability Letters, Elsevier, pages 223-230.

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