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Plug-in bandwidth selector for the kernel relative density estimator

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Abstract

This paper is focused on two kernel relative density estimators in a two-sample problem. An asymptotic expression for the mean integrated squared error of these estimators is found and, based on it, two solve- the-equation plug-in bandwidth selectors are proposed. In order to examine their practical performance a simulation study and a practical application to a medical dataset are carried out.

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References

  • Ahmad I.A. (2002). On moment inequalities of the supremum of empirical processes with applications to kernel estimation. Statistics & Probability Letters 57, 215–220

    Article  MATH  MathSciNet  Google Scholar 

  • Cao R., Janssen P., Veraverbeke N. (2000). Relative density estimation with censored data. The Canadian Journal of Statistics 28, 97–111

    Article  MATH  MathSciNet  Google Scholar 

  • Cao R., Janssen P., Veraverbeke N. (2001). Relative density estimation and local bandwidth selection for censored data. Computational Statistics & Data Analysis 36, 497–510

    MATH  MathSciNet  Google Scholar 

  • Ćwik J., Mielniczuk J. (1993). Data-dependent bandwidth choice for a grade density kernel estimate. Statistics & Probability Letters 16, 397–405

    Article  MathSciNet  Google Scholar 

  • Gastwirth J.L. (1968). The first-median test: A two-sided version of the control median test. Journal of the American Statistical Association 63, 692–706

    Article  MATH  MathSciNet  Google Scholar 

  • Hall P., Marron J.S. (1987). Estimation of integrated squared density derivatives. Statistics & Probability Letters 6, 109–115

    Article  MATH  MathSciNet  Google Scholar 

  • Handcock M., Janssen P. (2002). Statistical inference for the relative density. Sociological Methods & Research 30, 394–424

    Article  MathSciNet  Google Scholar 

  • Hjort N.L., Walker SG. (2001). A note on kernel density estimators with optimal bandwidths. Statistics & Probability Letters 54, 153–159

    Article  MATH  MathSciNet  Google Scholar 

  • Holmgren EB. (1996). The PP plot as a method for comparing treatment effects. Journal of the American Statistical Association 90, 360–365

    Article  Google Scholar 

  • Hsieh F. (1995). The empirical process approach for semiparametric two-sample models with heterogenous treatment effect. Journal of the Royal Statistical Society. Series B 57, 735–748

    MATH  MathSciNet  Google Scholar 

  • Hsieh F., Turnbull BW. (1996). Nonparametric and semiparametric estimation of the receiver operating characteristic curve. The Annals of Statistics 24, 25–40

    Article  MATH  MathSciNet  Google Scholar 

  • Kakizawa Y. (2004). Bernstein polynomial probability density estimation. Journal of Nonparametric Statistics 16, 709–729

    Article  MATH  MathSciNet  Google Scholar 

  • Li G., Tiwari R.C., Wells M.T. (1996). Quantile comparison functions in two-sample problems with applications to comparisons of diagnostic markers. Journal of the American Statistical Association 91, 689–698

    Article  MATH  MathSciNet  Google Scholar 

  • Polansky A.M., Baker ER. (2000). Multistage plug-in bandwidth selection for kernel distribution function estimates. Journal of Statistical Computation & Simulation 65, 63–80

    Article  MATH  MathSciNet  Google Scholar 

  • Sheather S.J., Jones MC. (1991). A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B 53, 683–690

    MATH  MathSciNet  Google Scholar 

  • Silverman B.W. (1978). Density ratios, empirical likelihood and cot death. Applied Statistics 27, 26–33

    Article  Google Scholar 

  • Wand M.P., Jones M.C. (1995). Kernel Smoothing. London, Chapman and Hall

    MATH  Google Scholar 

Download references

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Correspondence to Elisa María Molanes-López.

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Molanes-López, E.M., Cao, R. Plug-in bandwidth selector for the kernel relative density estimator. AISM 60, 273–300 (2008). https://doi.org/10.1007/s10463-006-0108-y

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  • DOI: https://doi.org/10.1007/s10463-006-0108-y

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