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

Author

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

Abstract

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. Firpo, Sergio & Galvao, Antonio F. & Song, Suyong, 2017. "Measurement errors in quantile regression models," Journal of Econometrics, Elsevier, vol. 198(1), pages 146-164.
    2. 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.
    3. 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.
    4. 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.
    5. Ying Liu & Dootika Vats & James M. Flegal, 2022. "Batch Size Selection for Variance Estimators in MCMC," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 65-93, March.
    6. José E. Chacón & Carlos Tenreiro, 2012. "Exact and Asymptotically Optimal Bandwidths for Kernel Estimation of Density Functionals," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 523-548, September.
    7. 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.
    8. 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.
    9. Bissantz, Nicolai & Holzmann, Hajo, 2007. "Statistical inference for inverse problems," Technical Reports 2007,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    10. Arthur Berg & Dimitris Politis & Kagba Suaray & Hui Zeng, 2020. "Reduced bias nonparametric lifetime density and hazard estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 704-727, September.
    11. Susanne M Schennach, 2020. "A Bias Bound Approach to Non-parametric Inference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(5), pages 2439-2472.
    12. Gregory Rice & Han Lin Shang, 2017. "A Plug-in Bandwidth Selection Procedure for Long-Run Covariance Estimation with Stationary Functional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 591-609, July.
    13. Dimitris N. Politis & Peter F. Tarassenko & Vyacheslav A. Vasiliev, 2022. "Estimating Smoothness and Optimal Bandwidth for Probability Density Functions," Stats, MDPI, vol. 6(1), pages 1-20, December.
    14. Guillermo Basulto-Elias & Alicia L. Carriquiry & Kris Brabanter & Daniel J. Nordman, 2021. "Bivariate Kernel Deconvolution with Panel Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 122-151, May.
    15. 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.
    16. 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.
    17. 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.
    18. Langrené, Nicolas & Warin, Xavier, 2021. "Fast multivariate empirical cumulative distribution function with connection to kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).

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