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A New Smooth Density Estimator for Non-Negative Random Variables

Title:

A New Smooth Density Estimator for Non-Negative Random Variables

Chaubey, Yogendra P. and Sen, Arusharka and Sen, Pranab K. (2007) A New Smooth Density Estimator for Non-Negative Random Variables. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.

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Abstract

Commonly used kernel density estimators may not provide admissible values of the density or its functionals at the boundaries for densities with restricted support. For smoothing the empirical distribution a generalization of the Hille's lemma, considered here, alleviates some of the problems of kernel density estimator near the boundaries. For nonnegative random variables which crop up in reliability and survival analysis, the proposed procedure is
thoroughly explored; its consistency and asymptotic distributional results are established under appropriate regularity assumptions. Methods of obtaining smoothing parameters
through cross-validation are given, and graphical illustrations of the estimator for continuous
(at zero) as well as discontinuous densities are provided.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Monograph (Technical Report)
Authors:Chaubey, Yogendra P. and Sen, Arusharka and Sen, Pranab K.
Series Name:Department of Mathematics & Statistics. Technical Report No. 1/07
Corporate Authors:Concordia University. Department of Mathematics & Statistics
Institution:Concordia University
Date:January 2007
Keywords:Asymptotics; boundary correction; cross-validation; empirical distribution; hazard function; Hille's lemma; kernel density estimator; survival function
ID Code:6681
Deposited By:DIANE MICHAUD
Deposited On:03 Jun 2010 16:45
Last Modified:08 Dec 2010 18:20
References:
Bagai, I. and Prakasa Rao, B.L.S. (1996). Kernel Type Density Estimates for Positive Valued Random Variables. Sankhya, A57 56-67.

Bouezmarni, Taou¯k; Scaillet, Olivier (2005). Consistency of asymmetric kernel density estimators and smoothed histograms with application to income data. Econometric
Theory, 21, 390-412.

Chaubey, Y. P., and Sen, P. K. (1996). On smooth estimation of survival and density functions. Statist. Decisions, 14, 1-22.

Chen, S. X. (2000). Probability density function estimation using Gamma kernels. An.n.Inst. Statist. Meth. 52, 471-480.

Chung, K. L. (1974). A course in probability theory (2nd ed.). Academic Press, New York and London.

Devroye, L. (1989) A Course in Density Estimation. Birkh}auser, Boston.

Eubank, R.L. (1988) Spline Smoothing and Nonparametric Regression, Marcel Dekker, New York.

Feller, W. (1965) An Introduction to Probability Theory and its Applications, Vol. II. John Wiley and Sons, New York.

Hille, E. (1948)Functional Analysis and Semigroups, Am. Math. Colloq. Pub 31, New York.

Marron, J. S., Ruppert, D. (1994). Transformations to reduce boundary bias in kernel density estimation. J. Roy. Statist. Soc. Ser. B 56, 653-671.

Parzen, E. (1962) On estimation of probability density and mode. Ann. Math Statist., 33, 1065-1070.

Rosenblatt, M. (1956) Remarks on some nonparametric estimates of density functions. Ann. Math Statist., 27 832-837.

Ruppert, D. and Wand, M. P. (1992). Correcting for kurtosis in density estimation. Australian Journal of Statistics, 34, 1929.

Scaillet, O. (2004). Density estimation using inverse Gaussian and reciprocal inverse Gaussian kernels. Journal of Nonparametric Statistics, 16, 217-226.

Scott, D. W. (1992). Multivariate Density Estimation. Theory, Practice and Visualizations. New York: John Wiley and Sons.

Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. London: Chapman and Hall.

Wand, M.P. and Jones, M.C. (1995). Kernel Smoothing. London: Chapman and Hall.

Wand, M.P., Marron, J.S. and Ruppert, D. (1991). Transformations in density estimation. Journal of the American Statistical Association, 86, 343-361.
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