Wavelet Density Estimation of Censoring Data and Evaluate of Mean Integral Square Error with Convergence Ratio and Empirical Distribution of Given Estimator

Mahmoud Afshari^{*}

Show more

References

[1] Harr, A. (1910) Zur Theorie der Orthogonalen Funktionen. Mathematische Annalen, 69, 331-371.

[2] Daubechies, I. (1988) Orthogonal Bases of Compactly Supported Wavelets. Communication in Pure and Applied Mathematics, 41, 909-996.

[3] Antoniadis, A. (1996) Smoothing Noisy Data with Tapered Coiflets Series. Scandinavian Journal of Statistics, 23, 313-330.

[4] Afshari, M. (2013) A Fast Wavelet Algorithm for Analyzing of Signal Processing and Empirical Distribution of Wavelet Coefficients with Numerical Example and Simulation. Communication of Statistics-Theory and Methods, 42, 4156-4169.

[5] Afshari, M. (2014) Estimation of Hazard Function for Censoring Random Variable by Using Wavelet Decomposition and Evaluate of MISE, AMSE With Simulation. Journal of Data Analysis and Information Processing, 2, 1-5.

http://dx.doi.org/10.4236/jdaip.2014.21001

[6] Afshari, M. (2008) Wavelet-Kernel Estimation of Regression Function for Uniformly Mixing Process. Word Applied Sciences Journal, 4, 605-609.

[7] Donoha, D.L. and Johnstone, I.M. (1994) Ideal Spatial Adaptation by Wavelet Shrinkage. Biometrika Journal, 81, 425-455.

http://dx.doi.org/10.1093/biomet/81.3.425

[8] Kerkyacharian, G. and Picard, D. (1993) Density Estimation Bykernel and Probability. McGraw-Hill Science, New York, 327-336.

[9] Mallat, S.G. (1989) A Theory for Multiresolution Signal Decomposition: The Wavelet Representation. Transformations on Pattern Analysis and Machine Intelligence, 11, 674-693.

[10] Meyer, Y. (1990) On de lettes et operateurs. Hermann, Paris.

[11] Hall, P. and Patil, P. (1995) Formula for Mean Integrated Squarederror of Non-Linear Wavelet Based Density Estimators. Annals of Statistics, 23, 905-928.

http://dx.doi.org/10.1214/aos/1176324628

[12] Antoniadis, A., Gregoire, G. and Nason, P. (1999) Density and Hazard Rate Estimation for Right Censored Data Using Wavelet Methods. Journal of Royal Statistical Society Series B, 23, 313-330.

[13] Vidakovik, B. (1999) Statistical Modeling by Wavelets. Wiley, New York.

http://dx.doi.org/10.1002/9780470317020