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Local-moment nonparametric density estimation of pre-binned data

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  • Papkov, Galen I.
  • Scott, David W.

Abstract

Data-driven research is often hampered by privacy restrictions in the form of limited data sets or graphical representations without the benefit of raw data. Nonparametric techniques that circumvent these issues by using local moment information, thereby extending the piecewise-polynomial histograms, are developed. These methods utilize not only binned data counts, but also their conditional moments in order to better estimate the underlying density of the data. A particular polynomial spline density estimator can be found via penalized least-squares optimization with a roughness penalty. Two issues exist in regards to the original algorithm: (1) local moments for empty bins are undefined and (2) all moment information is treated equally, despite the fact that lower-order moments are more accurate than higher-order moments. Solutions to both issues are provided by using unconditional moments and incorporating a weight matrix into the optimization problem.

Suggested Citation

  • Papkov, Galen I. & Scott, David W., 2010. "Local-moment nonparametric density estimation of pre-binned data," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3421-3429, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3421-3429
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    2. Koo, Ja-Yong & Kooperberg, Charles, 2000. "Logspline density estimation for binned data," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 133-147, January.
    3. Zhou S. & Shen X., 2001. "Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 247-259, March.
    4. 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.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
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    1. Lambert, Philippe, 2023. "Nonparametric density estimation and risk quantification from tabulated sample moments," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 177-189.

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