Estimation of Hazard Function for Censoring Random Variable by Using Wavelet Decomposition and Evaluation of MISE, AMSE with Simulation

Affiliation(s)

Department of Statistics, College of Science, Persian Gulf University, Bushehr, Iran.

Department of Statistics, College of Science, Persian Gulf University, Bushehr, Iran.

ABSTRACT

Wavelet analysis is one of the mostly new methods of pure and applied mathematics science. In this paper, we use the wavelet method to estimate the hazard function for censoring random variable. We consider the convergence ratio of given estimator. Also we present the simulation in order to test purpose estimator by calculating the mean integrated squared error (MISE) and average mean squared error (AMSE).

Cite this paper

M. Afshari and S. Tahmasebi, "Estimation of Hazard Function for Censoring Random Variable by Using Wavelet Decomposition and Evaluation of MISE, AMSE with Simulation,"*Journal of Data Analysis and Information Processing*, Vol. 2 No. 1, 2014, pp. 1-5. doi: 10.4236/jdaip.2014.21001.

M. Afshari and S. Tahmasebi, "Estimation of Hazard Function for Censoring Random Variable by Using Wavelet Decomposition and Evaluation of MISE, AMSE with Simulation,"

References

[1] A. Haar, “Zur Thorie der Orthogonal Functioned-System,” Annals of Mathematics, Vol. 69, No. 3, 1910, pp. 331-371. http://dx.doi.org/10.1007/BF01456326

[2] P. Doukhan, “Mixing Properties and Examples,” Springer-Verlag, New York, 1995.

[3] A. Antoniadis, “Smoothing Noisy Data with Tapered Coiflet Series,” Scandinavian Journal of Statistics, Vol. 23, 1996, pp. 313-330.

[4] S. G. Mallat, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, 1989, pp. 674-693. http://dx.doi.org/10.1109/34.192463

[5] Y. Meyer, “Ondelettes et Operateurs,” Hermann, Paris, 1990.

[6] I. Daubechies, “Ten Lectures on Wavelets,” SIAM, Philadelphia, 1992.

[7] D. L. Donoha and I. M. Johnstone, “Ideal Spatial Adaptation by Wavelet Shrinkage,” Biometrika Journal, Vol. 81, No. 3, 1994, pp. 425-455. http://dx.doi.org/10.1093/biomet/81.3.425

[8] G. Kerkyacharian and D. Picard, “Density Estimation by Kernel,” Probability and Letters, Vol. 18, No. 4, 1993, pp. 327-336. http://dx.doi.org/10.1016/0167-7152(93)90024-D

[9] P. Hall and P. Patil, “Formula for Mean Integrated Squared Error of Non-Linear Wavelet Based Density Estimators,” Annals of Statistics, Vol. 23, No. 3, pp. 905-928. http://dx.doi.org/10.1214/aos/1176324628

[10] A. Antoniadis, G. Gregoire and G. P. Nason, “Density and Harzard Rate Estimation for Right Censored Data Using Wavelet Methods,” Journal of Royal Statistical Society, Series B, Vol. 61, No. 1, 1999, pp. 63-84. http://dx.doi.org/10.1111/1467-9868.00163

[11] I. Daubechies, “Orthogonal Bases of Compactly Supported Wavelets,” Communication in Pure and Applied Mathematics, Vol. 41, No. 7, 1988, pp. 909-996. http://dx.doi.org/10.1002/cpa.3160410705

[12] M. Afshari, “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, Vol. 42, No. 22, 2013, pp. 4156-4169. http://dx.doi.org/10.1080/03610926.2011.642917

[13] M. Afshari, “Wavelet Density Estimation of Censoring Data and Evaluate of Mean Integral Square Error with Convergence Ratio and Empirical Distribution of Given Estimator,” 2013, under print.

[14] H. Doosti, M. Afshari and H. A. Niroomand, “Wavelets for Nonparametric Stochastic Regression with Mixing Stochastic Process,” Communication of Statistics-Theory and Methods, Vol. 37, No. 3, 2008, pp. 373-385. http://dx.doi.org/10.1080/03610920701653003

[1] A. Haar, “Zur Thorie der Orthogonal Functioned-System,” Annals of Mathematics, Vol. 69, No. 3, 1910, pp. 331-371. http://dx.doi.org/10.1007/BF01456326

[2] P. Doukhan, “Mixing Properties and Examples,” Springer-Verlag, New York, 1995.

[3] A. Antoniadis, “Smoothing Noisy Data with Tapered Coiflet Series,” Scandinavian Journal of Statistics, Vol. 23, 1996, pp. 313-330.

[4] S. G. Mallat, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, 1989, pp. 674-693. http://dx.doi.org/10.1109/34.192463

[5] Y. Meyer, “Ondelettes et Operateurs,” Hermann, Paris, 1990.

[6] I. Daubechies, “Ten Lectures on Wavelets,” SIAM, Philadelphia, 1992.

[7] D. L. Donoha and I. M. Johnstone, “Ideal Spatial Adaptation by Wavelet Shrinkage,” Biometrika Journal, Vol. 81, No. 3, 1994, pp. 425-455. http://dx.doi.org/10.1093/biomet/81.3.425

[8] G. Kerkyacharian and D. Picard, “Density Estimation by Kernel,” Probability and Letters, Vol. 18, No. 4, 1993, pp. 327-336. http://dx.doi.org/10.1016/0167-7152(93)90024-D

[9] P. Hall and P. Patil, “Formula for Mean Integrated Squared Error of Non-Linear Wavelet Based Density Estimators,” Annals of Statistics, Vol. 23, No. 3, pp. 905-928. http://dx.doi.org/10.1214/aos/1176324628

[10] A. Antoniadis, G. Gregoire and G. P. Nason, “Density and Harzard Rate Estimation for Right Censored Data Using Wavelet Methods,” Journal of Royal Statistical Society, Series B, Vol. 61, No. 1, 1999, pp. 63-84. http://dx.doi.org/10.1111/1467-9868.00163

[11] I. Daubechies, “Orthogonal Bases of Compactly Supported Wavelets,” Communication in Pure and Applied Mathematics, Vol. 41, No. 7, 1988, pp. 909-996. http://dx.doi.org/10.1002/cpa.3160410705

[12] M. Afshari, “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, Vol. 42, No. 22, 2013, pp. 4156-4169. http://dx.doi.org/10.1080/03610926.2011.642917

[13] M. Afshari, “Wavelet Density Estimation of Censoring Data and Evaluate of Mean Integral Square Error with Convergence Ratio and Empirical Distribution of Given Estimator,” 2013, under print.

[14] H. Doosti, M. Afshari and H. A. Niroomand, “Wavelets for Nonparametric Stochastic Regression with Mixing Stochastic Process,” Communication of Statistics-Theory and Methods, Vol. 37, No. 3, 2008, pp. 373-385. http://dx.doi.org/10.1080/03610920701653003