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Multivariate Density Estimation with General Flat-Top Kernels of Infinite Order


  • Politis, Dimitris N.
  • Romano, Joseph P.


The problem of nonparametric estimation of a multivariate density function is addressed. In particular, a general class of estimators with favorable asymptotic performance (bias, variance, rate of convergence) is proposed. The proposed estimators are characterized by the flatness near the origin of the Fourier transform of the kernel and are actually shown to be exactly-consistent provided the density is sufficiently smooth.

Suggested Citation

  • Politis, Dimitris N. & Romano, Joseph P., 1999. "Multivariate Density Estimation with General Flat-Top Kernels of Infinite Order," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 1-25, January.
  • Handle: RePEc:eee:jmvana:v:68:y:1999:i:1:p:1-25

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    Cited by:

    1. McMurry, Timothy L. & Politis, Dimitris N., 2008. "Bootstrap confidence intervals in nonparametric regression with built-in bias correction," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2463-2469, October.
    2. Schennach, Susanne & White, Halbert & Chalak, Karim, 2012. "Local indirect least squares and average marginal effects in nonseparable structural systems," Journal of Econometrics, Elsevier, vol. 166(2), pages 282-302.
    3. Horváth, Lajos & Rice, Gregory & Whipple, Stephen, 2016. "Adaptive bandwidth selection in the long run covariance estimator of functional time series," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 676-693.
    4. Firpo, Sergio & Galvao, Antonio F. & Song, Suyong, 2017. "Measurement errors in quantile regression models," Journal of Econometrics, Elsevier, vol. 198(1), pages 146-164.
    5. Hassan Doosti & Peter Hall, 2016. "Making a non-parametric density estimator more attractive, and more accurate, by data perturbation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 445-462, March.
    6. Bissantz, Nicolai & Holzmann, Hajo, 2007. "Statistical inference for inverse problems," Technical Reports 2007,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Susanne M. Schennach, 2015. "A bias bound approach to nonparametric inference," CeMMAP working papers CWP71/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. repec:bla:jtsera:v:38:y:2017:i:4:p:591-609 is not listed on IDEAS
    9. Susanne Schennach & Halbert White & Karim Chalak, 2007. "Local Indirect Least Squares and Average Marginal Effects in Nonseparable Structural Systems," Boston College Working Papers in Economics 680, Boston College Department of Economics, revised 26 Dec 2009.
    10. Canay, Ivan A., 2010. "Simultaneous selection and weighting of moments in GMM using a trapezoidal kernel," Journal of Econometrics, Elsevier, vol. 156(2), pages 284-303, June.
    11. Bissantz, Nicolai & Dümbgen, Lutz & Holzmann, Hajo & Munk, Axel, 2007. "Nonparametric confidence bands in deconvolution density estimation," Technical Reports 2007,03, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    12. Holzmann, Hajo & Bissantz, Nicolai & Munk, Axel, 2007. "Density testing in a contaminated sample," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 57-75, January.


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