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

Author

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  • Jones, M. C.
  • Sheather, S. J.

Abstract

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.

Suggested Citation

  • Jones, M. C. & Sheather, S. J., 1991. "Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 511-514, June.
  • Handle: RePEc:eee:stapro:v:11:y:1991:i:6:p:511-514
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    Cited by:

    1. Hidehiko Ichimura & Oliver Linton, 2001. "Asymptotic expansions for some semiparametric program evaluation estimators," CeMMAP working papers CWP04/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. 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.
    3. Mizushima, Takamasa, 2000. "Multisample tests for scale based on kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 81-91, August.
    4. repec:spr:stmapp:v:10:y:2001:i:1:d:10.1007_bf02511640 is not listed on IDEAS
    5. Berwin A. TURLACH, "undated". "Bandwidth selection in kernel density estimation: a rewiew," Statistic und Oekonometrie 9307, Humboldt Universitaet Berlin.
    6. Wang, Qing & Lindsay, Bruce G., 2015. "Improving cross-validated bandwidth selection using subsampling-extrapolation techniques," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 51-71.
    7. Y. K. Tseng & Y. R. Su & M. Mao & J. L. Wang, 2015. "An extended hazard model with longitudinal covariates," Biometrika, Biometrika Trust, vol. 102(1), pages 135-150.
    8. 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.
    9. Moreira, C. & Van Keilegom, I., 2013. "Bandwidth selection for kernel density estimation with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 107-123.
    10. Tiee-Jian Wu & Chih-Yuan Hsu & Huang-Yu Chen & Hui-Chun Yu, 2014. "Root $$n$$ n estimates of vectors of integrated density partial derivative functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 865-895, October.
    11. 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.
    12. repec:eee:reensy:v:147:y:2016:i:c:p:109-116 is not listed on IDEAS
    13. repec:bla:biomet:v:73:y:2017:i:1:p:114-123 is not listed on IDEAS
    14. 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.
    15. 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;Sociedad de Estadística e Investigación Operativa, vol. 6(2), pages 223-320, December.
    16. 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.
    17. 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.
    18. 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.
    19. repec:spr:testjl:v:26:y:2017:i:3:d:10.1007_s11749-017-0523-9 is not listed on IDEAS
    20. Dimitrios Bagkavos, 2011. "Local linear hazard rate estimation and bandwidth selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 1019-1046, October.
    21. 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.
    22. 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.

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