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Total error in a plug-in estimator of level sets

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  • Baíllo, Amparo

Abstract

Given a density f, the minimum volume set of probability [alpha] can be estimated by the corresponding minimum volume set of a kernel estimator. We obtain convergence rates for this set estimator with respect to a measure-based distance.

Suggested Citation

  • Baíllo, Amparo, 2003. "Total error in a plug-in estimator of level sets," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 411-417, December.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:4:p:411-417
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    References listed on IDEAS

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    1. Baíllo, Amparo & Cuesta-Albertos, Juan A. & Cuevas, Antonio, 2001. "Convergence rates in nonparametric estimation of level sets," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 27-35, May.
    2. Einmahl, J. H.J. & Mason, D.M., 1992. "Generalized quantile processes," Other publications TiSEM b2a76bac-045d-457f-869f-d, Tilburg University, School of Economics and Management.
    3. Ilya S. Molchanov, 1998. "A Limit Theorem for Solutions of Inequalities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 235-242, March.
    4. Polonik, Wolfgang, 1997. "Minimum volume sets and generalized quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 69(1), pages 1-24, July.
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    Cited by:

    1. Baíllo, Amparo & Cuevas, Antonio, 2003. "Parametric versus nonparametric tolerance regions indetection problems," DES - Working Papers. Statistics and Econometrics. WS ws037017, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Cholaquidis, Alejandro & Fraiman, Ricardo & Moreno, Leonardo, 2022. "Level set and density estimation on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Mammen, Enno & Polonik, Wolfgang, 2013. "Confidence regions for level sets," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 202-214.
    4. Chiwoo Park & Jianhua Z. Huang & Yu Ding, 2010. "A Computable Plug-In Estimator of Minimum Volume Sets for Novelty Detection," Operations Research, INFORMS, vol. 58(5), pages 1469-1480, October.
    5. J Morio & R Pastel, 2012. "Plug-in estimation of d-dimensional density minimum volume set of a rare event in a complex system," Journal of Risk and Reliability, , vol. 226(3), pages 337-345, June.

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