Comparison of optimal bandwidths for some density estimators
Keywords:
Density Estimation, Histogram, Kernel Density EstimationAbstract
Density estimation is a classic problem and has been extensively studied in Statistics. In this paper we briefly review some usual density estimators as the histogram, the Averaged Shifted Histograms (ASH) and the kernel density estimator (Kde). We care in particular on the choice of the bandwidth of Kde which is a fundamental parameter of the model and greatly influences the prediction. We finished our work with a simulation comparing the described methods on a common set of densities.
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References
[1] W. Härdle, M. Müller, S. Sperlich, and A. Werwatz. Nonparametric and Semiparametric Models.Springer Verlag, Heidelberg, 2004.
[2] D.W. Scott. Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley series in probability and mathematical statistics: Applied probability and statistics. Wiley, 1992.
[3] B. W. Silverman. Density Estimation for Statistics and Data Analysis. Chapman and Hall, London, 1986.
[4] M. Rosenblatt. Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, 27:832–837, 1956.
[5] A. Bowman. An alternative method of cross-validation for the smoothing of density estimates. Biometrika, 71:353–36, 1984.
[6] C. Stone. An asymptotically optimal window selection rule for kernel density estimates. The Annals of Statisitics, 12:1285–1297, 1984.
[7] S. J. Sheather and M. C. Jones. A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society, Series B, Methodological, 53:683–690, 1991.
[8] S.J. Sheather. Density estimation. Statistical Science, 19(4):588–597, 2004.
[9] M. Bourel. Metodos de agregacion de modelos y aplicaciones. Memoria de trabajos de difusion cientifica y tecnica, 10:19–32, 2012.
[10] M. Bourel, R. Fraiman, and B. Ghattas. Random average shifted histogram. To appear, 2013.
[11] M. Bourel and B. Ghattas. Aggregating density estimators: an empirical study. Open Journal of Statistics, 3(5), 2013.
[12] M. Di Marzio and C.C. Taylor. Boosting kernel density estimates: A bias reduction technique? Biometrika, 91(1):226–233, 2004.
[13] D.W Scott. Averaged shifted histogram: Effective nonparametric density estimators inseveral dimensions. The Annals of Statistics, 13(3):1024–1040, 1985.
[14] M. Bourel. Apprentissage statistique par agrégation de modèles pour l’estimation de la densité et la classification multiclasse. Tesis Université Aix-Marseille, France, 2013.
[2] D.W. Scott. Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley series in probability and mathematical statistics: Applied probability and statistics. Wiley, 1992.
[3] B. W. Silverman. Density Estimation for Statistics and Data Analysis. Chapman and Hall, London, 1986.
[4] M. Rosenblatt. Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, 27:832–837, 1956.
[5] A. Bowman. An alternative method of cross-validation for the smoothing of density estimates. Biometrika, 71:353–36, 1984.
[6] C. Stone. An asymptotically optimal window selection rule for kernel density estimates. The Annals of Statisitics, 12:1285–1297, 1984.
[7] S. J. Sheather and M. C. Jones. A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society, Series B, Methodological, 53:683–690, 1991.
[8] S.J. Sheather. Density estimation. Statistical Science, 19(4):588–597, 2004.
[9] M. Bourel. Metodos de agregacion de modelos y aplicaciones. Memoria de trabajos de difusion cientifica y tecnica, 10:19–32, 2012.
[10] M. Bourel, R. Fraiman, and B. Ghattas. Random average shifted histogram. To appear, 2013.
[11] M. Bourel and B. Ghattas. Aggregating density estimators: an empirical study. Open Journal of Statistics, 3(5), 2013.
[12] M. Di Marzio and C.C. Taylor. Boosting kernel density estimates: A bias reduction technique? Biometrika, 91(1):226–233, 2004.
[13] D.W Scott. Averaged shifted histogram: Effective nonparametric density estimators inseveral dimensions. The Annals of Statistics, 13(3):1024–1040, 1985.
[14] M. Bourel. Apprentissage statistique par agrégation de modèles pour l’estimation de la densité et la classification multiclasse. Tesis Université Aix-Marseille, France, 2013.
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Published
2013-12-02
How to Cite
[1]
M. Bourel, “Comparison of optimal bandwidths for some density estimators”, Memoria investig. ing. (Facultad Ing., Univ. Montev.), no. 11, pp. 59–74, Dec. 2013.
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