Nonparametric Least Squares Mixture Density Estimation
DOI:
https://doi.org/10.11113/jt.v63.1905Keywords:
Nonparametric mixtures, least squares estimation, kernel density estimation, bandwidth selection, cross-validationAbstract
In this paper, we consider using nonparametric mixtures for density estimation. The mixture density estimation problem simply reduces to the problem of estimating a mixing distribution in the nonparametric mixture model. We focus on the least squares method for mixture density estimation problem. In a simulation experiment, the performance of the least squares mixture density estimator (MDE) and the kernel density estimator (KDE) is assessed by the mean integrated squared error. The performance improvement of MDE over KDE for some common densities is achieved by using cross-validation method for bandwidth selection.
References
Balabdaoui, F. and Wellner, J. A. 2010. Estimation of a k-monotone Density: Characterizations, Consistency and Minimax Lower Bounds. Statistica Neerlandica. 64(1): 45–70.
BÓ§hning, D. 2000. Computer-Assisted Analysis of Mixtures and Applications: Meta-Analysis, Disease Mapping and Others. London: Chapman and Hall.
Dax, A. (1990) The Smallest Point of a Polytope. Journal of Optimization Theory and Applications. 64(2): 429–432.
Eggermont, P. P. B. and LaRiccia, V. N. 2001 Maximum Penalized Likelihood Estimation. Volume I: Density Estimation. New York: Springer.
Jones, M. C. and Henderson, D. A. 2009 Maximum Likelihood Kernel Density Estimation: On the Potential of Convolution Sieves. Computational Statistics and Data Analysis. 53(10): 3726–3733.
Jones, M. C., Marron, J. S. and Sheather, S. J. 1996. A Brief Survey of Bandwidth Selection for Density Estimation. Journal of the American Statistical Association. 91(433): 401–407.
Lawson, C. L. and Hanson, R. J. 1974. Solving Least Squares Problems. Englewood Cliffs: Prentice-Hall Inc.
Lindsay, B. G. 1995. Mixture Models: Theory, Geometry and Applications, vol. 5 of NSF-CBMS Regional Conference Series in Probability and Statistics. Hayward: Institute of Mathematical Statistics.
Loader, C. R. 1999. Bandwidth selection: Classical or plug-in? The Annals of Statistics. 27(2): 415–438.
Marron, J. S. and Wand, M. P. 1992. Exact Mean Integrated Squared Error. The Annals of Statistics. 20(2): 712–736.
Priebe, C. E. and Marchette, D. J. 2000. Alternating Kernel and Mixture Density Estimates. Computational Statistics and Data Analysis. 35(1): 43–65.
Roeder, K. M. and Wasserman, L. A. 1997. Practical Bayesian Density Estimation Using Mixtures of Normals. Journal of the American Statistical Association. 92(439): 894–902.
Scott, D. W. (2001) Parametric Statistical Modeling by Minimum Integrated Square Error. Technometrics. 43(3): 274–285.
Scott, D. W. and Szewczyk, W. F. 2001. From Kernels to Mixtures. Technometrics. 43(3): 323–335.
Silverman, B. W. 1986. Density Estimation for Statistics and Data Analysis. London: Chapman and Hall.
Wang, Y. 2007. On fast Computation of the Non-parametric Maximum Likelihood Estimate of a Mixing Distribution. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 69(2): 185–198.
Wang, Y. and Chee, C.-S. 2012. Density Estimation Using Non-parametric and Semi-parametric Mixtures. Statistical Modelling. 12(1): 67–92.
Yuan, M. 2009. State Price Density Estimation via Nonparametric Mixtures. The Annals of Applied Statistics. 3(3): 963–984.
Downloads
Published
Issue
Section
License
Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.
