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Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives


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  • Jones, M. C.
  • Sheather, S. J.
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    Improved kernel-based estimates of integrated squared density derivatives are obtained by reinstating non-stochastic terms that have previously been omitted, and using the bandwidth to (approximately) cancel these positive quantities with the leading smoothing bias terms which are negative. Such estimators have exhibited great practical merit in the context of data-based selection of the bandwidth in kernel density estimation, a motivating application of this work discussed elsewhere.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 11 (1991)
    Issue (Month): 6 (June)
    Pages: 511-514

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    Handle: RePEc:eee:stapro:v:11:y:1991:i:6:p:511-514

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    Keywords: Bandwidth selection bias reduction functional estimation kernel density estimation rates of convergence smoothing;


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    Cited by:
    1. Tenreiro, Carlos, 2003. "On the asymptotic normality of multistage integrated density derivatives kernel estimators," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 311-322, September.
    2. Powell, James L. & Stoker, Thomas M., 1992. "Optimal bandwidth choice for density-weighted averages," Working papers 3424-92., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Hidehiko Ichimura & Oliver Linton, 2003. "Asymptotic Expansions for Some Semiparametric Program Evaluation Estimators," STICERD - Econometrics Paper Series /2003/451, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Gonzalez-Manteiga, W. & Sanchez-Sellero, C. & Wand, M. P., 1996. "Accuracy of binned kernel functional approximations," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 1-16, June.
    5. Mizushima, Takamasa, 2000. "Multisample tests for scale based on kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 81-91, August.
    6. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December.
    7. Farmen, Mark & Marron, J. S., 1999. "An assessment of finite sample performance of adaptive methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 143-168, April.
    8. Hall, Peter & Wolff, Rodney C. L., 1995. "Estimators of integrals of powers of density derivatives," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 105-110, August.
    9. Dimitrios Bagkavos, 2011. "Local linear hazard rate estimation and bandwidth selection," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(5), pages 1019-1046, October.
    10. Hirukawa Masayuki, 2004. "A Two-Stage Plug-In Bandwidth Selection and Its Implementation in Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Working Papers 04005, Concordia University, Department of Economics.
    11. Saavedra, Ángeles & Cao, Ricardo, 1999. "Rate of convergence of a convolution-type estimator of the marginal density of a MA(1) process," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 129-155, April.
    12. Duc Devroye & J. Beirlant & R. Cao & R. Fraiman & P. Hall & M. Jones & Gábor Lugosi & E. Mammen & J. Marron & C. Sánchez-Sellero & J. Uña & F. Udina & L. Devroye, 1997. "Universal smoothing factor selection in density estimation: theory and practice," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 6(2), pages 223-320, December.
    13. Berwin A. TURLACH, . "Bandwidth selection in kernel density estimation: a rewiew," Statistic und Oekonometrie 9307, Humboldt Universitaet Berlin.
    14. Masayuki Hirukawa, 2006. "A Two-Stage Plug-In Bandwidth Selection and Its Implementation for Covariance Estimation," CIRJE F-Series CIRJE-F-431, CIRJE, Faculty of Economics, University of Tokyo.


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