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New approaches to nonparametric density estimation and selection of smoothing parameters


  • Golyandina, Nina
  • Pepelyshev, Andrey
  • Steland, Ansgar


The application of Singular Spectrum Analysis (SSA) to the empirical distribution function sampled at a grid of points spanning the range of the sample leads to a novel and promising method for the computer-intensive nonparametric estimation of both the distribution function and the density function. SSA yields a data-adaptive filter, whose length is a parameter that controls the smoothness of the filtered series. A data-adaptive algorithm for the automatic selection of a general smoothing parameter is introduced, which controls the number of modes of the estimated density. Extensive computer simulations demonstrate that the new automatic bandwidth selector improves on other popular methods for various densities of interest. A general uniform error bound is proved for the proposed SSA estimate of the distribution function, which ensures its uniform consistency. The simulation results indicate that the SSA density estimate with the automatic choice of the filter length outperforms the kernel density estimate in terms of the mean integrated squared error and the Kolmogorov–Smirnov distance for various density shapes. Two applications to problems arising in photovoltaic quality control and economic market research are studied to illustrate the benefits of SSA estimation.

Suggested Citation

  • Golyandina, Nina & Pepelyshev, Andrey & Steland, Ansgar, 2012. "New approaches to nonparametric density estimation and selection of smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2206-2218.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:7:p:2206-2218 DOI: 10.1016/j.csda.2011.12.019

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    References listed on IDEAS

    1. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    2. Savchuk, Olga Y. & Hart, Jeffrey D. & Sheather, Simon J., 2010. "Indirect Cross-Validation for Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 415-423.
    3. Lambert, Philippe & Eilers, Paul H.C., 2009. "Bayesian density estimation from grouped continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1388-1399, February.
    4. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
    5. Chan, Ngai-Hang & Lee, Thomas C.M. & Peng, Liang, 2010. "On nonparametric local inference for density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 509-515, February.
    6. Cheng, Cheng, 1995. "The Bernstein polynomial estimator of a smooth quantile function," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 321-330, September.
    7. Ansgar Steland & Henryk Zähle, 2009. "Sampling inspection by variables: nonparametric setting," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(1), pages 101-123.
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    Cited by:

    1. Calò, Daniela G. & Montanari, Angela & Viroli, Cinzia, 2014. "A hierarchical modeling approach for clustering probability density functions," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 79-91.
    2. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.
    3. Sreevani, & Murthy, C.A., 2016. "On bandwidth selection using minimal spanning tree for kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 67-84.
    4. Golyandina, Nina & Korobeynikov, Anton, 2014. "Basic Singular Spectrum Analysis and forecasting with R," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 934-954.


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