Wavelet Linear Estimation for Different Distributed Random Variables

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In this paper, we construct a wavelet linear estimator for the component of a finite mixture under independent identically distributed biased observations. We evaluate its performance by determining an upper bound of risk of function classes.

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3648-3652

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August 2013

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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[1] W. hardle, G. Kerkyacharian, D. Picard, A. Tsybakow, Wavelets, Approximation and Statistical Applications. Springer-Verlag, (1997).

Google Scholar

[2] B. L. S. Prakasa Rao, Wavelet linear density estimation for associated sequences, J. Indian Statist. Assoc., pp.369-379, (2003).

Google Scholar

[3] D. Pokhylko, Wavelet estimations of a density constructed from observations of a mixture, Theor. Probability and Math, no. 70, pp.135-145, (2005).

DOI: 10.1090/s0094-9000-05-00637-x

Google Scholar

[4] P. Chaubey and H. Doosti, Wavelet based estimation of the derivatives of a density with associated variables, Int. J. Pure and Appl. Math, no. 27, pp.97-106, (2006).

Google Scholar

[5] B. L. S. Prakasa Rao, Wavelet linear estimation for derivatives of a density from observations of a mixture with varying mixing proportions, Indian J. Pure Appl. Math, no. 41, pp.275-291, (2010).

DOI: 10.1007/s13226-010-0013-1

Google Scholar

[6] C. Chesneau, Wavelet linear estimation of a density and its derivatives from observations of a mixtures under quadrant dependence, hal-00510690, version 4-3, (2011).

Google Scholar

[7] S. Efromovich, Density estimation for biased data, The Annals of Statistics, no. 32, pp.1137-1161, (2004).

Google Scholar

[8] D. Donoho, I. Johnstone, G. Kerkyacharian, and D. Picard, Density estimation by wavelet thresholding , The Annals of Statistics, no. 24, pp.508-539, (1996).

DOI: 10.1214/aos/1032894451

Google Scholar

[9] H. Tribouley, Practical estimation of multivariate densities using wavelet methods , Statistics Neerlandica, no. 49, pp.41-62, (1995).

DOI: 10.1111/j.1467-9574.1995.tb01454.x

Google Scholar

[10] B. Vidakovic, Statistical Moseling by Wavelets, Wiley, New York, (1999).

Google Scholar