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Cross-validation and the smoothing of orthogonal series density estimators

Author

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  • Hall, Peter

Abstract

We describe a class of smoothed orthogonal series density estimates, including the classical sequential-series introduced by [6], Soviet Math. Dokl. 3 1559-1562) and [16], Ann. Math. Statist. 38 1261-1265), and [23], Ann. Statist 9 146-156) two-parameter smoothing. The Bowman-Rudemo method of least-squares cross-validation (1982, Manchester-Sheffield School of Probability and Statistics Research Report 84/AWB/1; 1984, Biometrika 71 353-360; [14], Scand. J. Statist. 9 65-78), is suggested as a practical way of choosing smoothing parameters automatically. Using techniques of [18], Ann. Statist. 12 1285-1297), that method is shown to perform asymptotically optimally in the case of cosine and Hermite series estimators. The same argument may be used for other types of series.

Suggested Citation

  • Hall, Peter, 1987. "Cross-validation and the smoothing of orthogonal series density estimators," Journal of Multivariate Analysis, Elsevier, vol. 21(2), pages 189-206, April.
    • Handle: RePEc:eee:jmvana:v:21:y:1987:i:2:p:189-206
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    Citations

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    Cited by:

    1. Jean-Marc Robin & Stéphane Bonhomme & Koen Jochmans, 2014. "Estimating Multivariate Latent-Structure Models," Sciences Po Economics Discussion Papers 2014-18, Sciences Po Departement of Economics.
    2. Yanchun Zhao & Mengzhu Zhang & Qian Ni & Xuhui Wang, 2023. "Adaptive Nonparametric Density Estimation with B-Spline Bases," Mathematics, MDPI, vol. 11(2), pages 1-12, January.
    3. repec:hal:spmain:info:hdl:2441/2i27dd3b6h94aarftq0slq652a is not listed on IDEAS
    4. Jean-Marc Robin & Stéphane Bonhomme & Koen Jochmans, 2014. "Estimating Multivariate Latent-Structure Models," Sciences Po Economics Discussion Papers 2014-18, Sciences Po Departement of Economics.
    5. Efromovich, Sam, 1996. "Adaptive orthogonal series density estimation for small samples," Computational Statistics & Data Analysis, Elsevier, vol. 22(6), pages 599-617, October.
    6. repec:hal:wpspec:info:hdl:2441/2i27dd3b6h94aarftq0slq652a is not listed on IDEAS
    7. repec:hal:spmain:info:hdl:2441/etefo8s8r89oamhnhiclqr530 is not listed on IDEAS
    8. Kirkby, J. Lars & Leitao, Álvaro & Nguyen, Duy, 2021. "Nonparametric density estimation and bandwidth selection with B-spline bases: A novel Galerkin method," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).

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