Laplace Dağılımının Ölçek Parametresi için Daraltıcı Tahmin ve Bootstrap Güven Aralığı

Bu çalışmada, Laplace dağılımının ölçek parametresi için yanlı bir tahmin edici önerilmiştir. İlk olarak, yanlı tahmin edicinin hata kare ortalamasının, maksimum olabilirlik tahmin edicisininkinden daha küçük olduğu teorik olarak gösterilmiştir. Daha sonra maksimum olabilirlik tahmin edicisi ile elde edilen yanlı tahminci, bu tahmincilerin göreli etkinilikleri kullanılarak bir benzetim çalışması ile karşılaştırılmıştır. Ayrıca tahmin edicileri farklı bir açıdan karşılaştırmak için Laplace dağılımının ölçek parametresi için bootstrap yöntemi ile güven aralıkları oluşturulmuştur.

Anahtar Kelimeler:

Bootstrap Güven Aralığı, Laplace Dağılımı, Daraltıcı Tahmin, Yanlı Tahmin

Shrinkage Estimation and Bootstrap Confidence Interval for Scale Parameter of Laplace Distribution

In this study, a biased estimator is proposed for the scale parameter of Laplace distribution. First, it is theoretically shown that the mean square error of the biased estimator is smaller than that of the maximum likelihood estimator. Then the maximum likelihood estimator is compared with the obtained biased estimator by means of a simulation study using the relative efficiency of these estimators. In addition, confidence intervals are constructed for the scale parameter of Laplace distribution with bootstrap method in order to compare them with each other in a different way.

Keywords:

Bootstrap Confidence Interval, Laplace Distribution, Biased Estimation, Shrinkage Estimation,

PDF

___

Akdoğan, Y., 2022. On the confidence intervals of process capability index Cpm based on a progressive type‐II censored sample. Quality and Reliability Engineering International, 38(5), 2845-2861.
Bain, L.J., and Engelhardt, M., 1973. Interval estimation for the two parameter Double Exponential distribution. Technometrics, 15, 875-887.
Balui, M., Deiri, E., Hormozinejad, F., and Jamkhaneh, E. B, 2020. Two different shrinkage estimator classes for the scale parameter of classical Rayleigh distribution. Microelectronic Engineering, 223, 111149.
Bhatnagar, S., 1986. On the use of population variance in estimating mean. Journal of the Indian Society of Agricultural Statistics, 38, 403-409.
Carpenter, J. and Bithell, J., 2000. Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians. Statistics in Medicine, 19, 1141-1164.
Chernick, M.R., 2008. Bootstrap Methods: A Guide For Practitioners And Researchers, Wiley
Chesneau, C., Karakaya, K., Bakouch, H. S., & Kuş, C. 2022. An Alternative to the Marshall-Olkin Family of Distributions: Bootstrap, Regression and Applications. Communications on Applied Mathematics and Computation, 4(4), 1229-1257.
Diaconis, P. and Efron, B., 1983. Computer-intensive methods in statistics. Scientific American, 248, 116-130.
DiCiccio, T.J. and Efron, B., 1996. Bootstrap confidence intervals. Statistical Science, 11(3), 189-228.
DiCiccio, T.J. and Tibshirani, R., 1987. Bootstrap confidence intervals and bootstrap approximations. Journal of the American statistical Association, 82(397), 163-170.
Ebegil, M. and Özdemir, Ş., 2016. Two Different Shrinkage Estimator Classes for the Shape Parameter of Classical Pareto Distribution. Hacettepe Journal of Mathematics and Statistics, 45(4), 1231-1244.
Efron, B., 1987. Better bootstrap confidence intervals. Journal of the American statistical Association, 82(397), 171 – 200.
Efron, B., and Tibshirani, R., 1986. Bootstrap methods for standard errors; confidence intervals and other measures of statistical accuracy. Statistical science,1, 54-77.
Efron, B., and Tibshirani, R., 1993. Introduction to the Bootstrap. Chapman & Hall.
Efron, B., 1979. Bootstrap methods; another look at the jackknife. Journal of the American Statistical Association, 7, 1-26.
Efron, B., and Gong, G., 1983. A Leisurely Look at the Bootstrap, the Jackknife, and Cross-Validation. The American Statistician, 37(1), 36-48.
Govindarajulu, Z., and Sahai, H., 1972. Estimation of the parameters of a normal distribution with known coefficient of variation. Reports of Statistical Application Research. Union of Japanese Scientists and Engineers, 1972, 91, 85-98.
Govindarajulu, Z., 1966. Best linear estimates under symmetric censoring of the parameters of the Double Exponential distribution. Journal of the American Statistical Association, 61(313), 248-258.
Jani, P.N., 1991. A class of shrinkage estimators for the scale parameter of the exponential distribution. IEEE Transactions on Reliability, 40, 68-70.
Mehta, J.S. and Srinivasan, S.R., 1971. Estimation of the mean by shrinkage to a point. Journal of the American Statistical Association, 66(233), 86-90.
Mehta, V., and Singh, H.P., 2014. Shrinkage Estimators of Parameters of Morgenstern Type Bivariate Logistic Distribution Using Ranked Set Sampling. Journal of Basic and Applied Engineering Research (JBAER), 1(13), 1-6.
Özdemir, Ş. and Ebegil, M., 2012. Shrinkage estimators for the shape parameter of classical Pareto distribution. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 16(1), 116-121. Park, L., 2011. Bootstrap confidence intervals for Mean Average Precision. Proceedings of the Fourth Annual ASEARC Conference Papers, 17-18 February University of Western Sydney, Paramatta, Australia.
Raughunandanan, K. and Srinivasan, R., 1971. Simplified estimation of parameters in a Double Exponential distribution. Technometrics, 13, 689-691.
Singh, H.P., and Mehta, V., 2016. A Class of Shrinkage Estimators of Scale Parameter of Uniform Distribution Based on K-Record Values. National Academy Science Letters, 39(3), 221-227.
Singh, H.P., Saxena, S., and Joshi, H., 2008. A family of shrinkage estimators for Weibull shape parameter in censored sampling. Statistical Papers, 49(3), 513-529.
Singh, H.P. and Saxena, S., 2003. A class of shrinkage estimators for variance of a normal population. Brazilian Journal of Probability and Statistics, 17, 41–56.
Singh, H.P. and Singh, R., 1997. A class of shrinkage estimators for the variance of a normal population. Microelectron and Reliability, 37(5), 863-867.
Singh, H.P. and Katyar, N.P., 1988. A generalized class of estimators for common parameters of two normal distribution with known coefficient of variation. Journal of the Indian Society of Agricultural Statistics, 40(2), 127-149.
Singh, H.P., 1990. Estimation of parameters in normal parent. Journal of the Indian Society of Agricultural Statistics, XL11(1), 98-107.
Thompson, J.R., 1968. Some shrinkage techniques for estimating the mean. Journal of the American Statistical Association, 63, 113-122.
Tiao, G.C., and Lund, D.R., 1970. The use of OLUMV estimators in inference robustness studies of the location parameter of a class of symmetric distributions. Journal of the American Statistical Association, 65, 370-388,
Vishwakarma, G.K., and Gupta, S., 2022. Shrinkage estimator for scale parameter of gamma distribution. Communications in Statistics-Simulation and Computation, 51(6), 3073-3080.