New approaches to nonparametric density estimation and selection of smoothing parameters
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Taoufik Bouezmarni & Jeroen V.K. Rombouts, 2006.
"Nonparametric Density Estimation for Positive Time Series,"
Cahiers de recherche
06-09, HEC Montréal, Institut d'économie appliquée.
- 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.
- BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V. K., 2006. "Nonparametric density estimation for positive time series," CORE Discussion Papers 2006085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- 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.
- 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.
- Cheng, Cheng, 1995. "The Bernstein polynomial estimator of a smooth quantile function," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 321-330, September.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:7:p:2206-2218. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.