Simulation Study The Implementation of Quantile Bootstrap Method on Autocorrelated Error

Ovi Delviyanti Saputri, Ferra Yanuar, Dodi Devianto


Quantile regression is a regression method with the approach of separating or dividing data into certain quantiles by minimizing the number of absolute values from asymmetrical errors to overcome unfulfilled assumptions, including the presence of autocorrelation. The resulting model parameters are tested for accuracy using the bootstrap method. The bootstrap method is a parameter estimation method by re-sampling from the original sample as much as R replication. The bootstrap trust interval was then used as a test consistency test algorithm constructed on the estimator by the quantile regression method. And test the uncommon quantile regression method with bootstrap method. The data obtained in this test is data replication 10 times. The biasness is calculated from the difference between the quantile estimate and bootstrap estimation. Quantile estimation methods are said to be unbiased if the standard deviation bias is less than the standard bootstrap deviation. This study proves that the estimated value with quantile regression is within the bootstrap percentile confidence interval and proves that 10 times replication produces a better estimation value compared to other replication measures. Quantile regression method in this study is also able to produce unbiased parameter estimation values.


Quantile Regression; Bootstrap Method; Autocorrelation Error

Full Text:



Bain, L. J., and Engelhardt, M. 1992. Introduction to Probability and Mathematical Statistics Second Edition. Duxbury Press, California.

Capinski, M., and Kopp, E. 2003. Measure, Integral, and Probability. Second Edition. Springer-Verlag, New York.

Casella, G., and Berger, R. L. 2002. Statistical Inference. Ed. Ke-2, Pasific Grove, California.

Chung, K. L. 2001. A Course In Probability Theory. Third Edition. Academy Press, Sandiego.

Davino, C., Furno, M., and Vistocco, D. 2014. Quantile Regression Theory and Aplications. Pondicherry, India.

Efron, B., and Tibshirani, J. R. 1993. An Introduction to the Bootstrap. New York: Champman and Hall, Inc.

Feng, X. 2011. Wild Bootstrap for Quantile Regression. Journal Biometrika 98, 4, 995-999.

Gujarati, D. N. 2003. Basic Econometrics. 4th Edition. The McGraw-Hill Companies, New Jersey.

Koenker, R., and Basset, G. J. 1978. Regression Quantiles. Econometrica, 46, 33-50.

Koenker, R. 2005. Quantile Regression. Cambridge University Press, New York.

Mansyur, A., Efendi, S., Firmansyah, and Togi. 2010. Estimator Parameter Model Regresi Linear dengan Metode Bootstrap. Jurnal Bulletin of Mathematics, 03, 189-202.

Oktafia, M., Yanuar, F., and Maiyastri. 2015. Simulasi Penduga Parameter Regresi Kuantil dengan Metode Bootstrap. Jurnal Matematika UNAND, 5(1), 125-130.



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Jalan Gajayana 50 Malang, Jawa Timur, Indonesia 65144
Faximile (+62) 341 558933

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.