Monte Carlo simulation of ordinary least squares estimator through linear regression adaptive refined descriptive sampling algorithm

References

• Aloui, A., and M. Ourbih-Tari. 2011. The use of refined descriptive sampling and applications in parallel Monte Carlo simulation. Computing and Informatics 30 (4):681–700.
   Web of Science ®Google Scholar
• Aloui, A., A. Zioui, M. Ourbih-Tari, and A. Alioui. 2015. A general purpose module using refined descriptive sampling for installation in simulation systems. Computational Statistics 30:477–90.
   Web of Science ®Google Scholar
• Baghdali-Ourbih, L., M. Ourbih-Tari, and A. Dahmani. 2017. I implementing refined descriptive sampling into three phase discrete-event simulation models. Communications in Statistics: Simulation and Computation 46 (5):4035–49.
   Web of Science ®Google Scholar
• Bianchi, A., and N. Salvati. 2015. Asymptotic properties and variance estimators of the M-quantile regression coefficients estimators. Communications in Statistics: Theory and Methods 44 (11):2416–29.
   Web of Science ®Google Scholar
• Cario, M. C., and B. L. Nelson. 1998. Numerical methods for fitting and simulating autoregressive-to-anything processes. INFORMS Journal on Computing 1:72–81.
   Google Scholar
• Clark, C. E. 1961. Importance sampling in Monte Carlo analyses. Operations research 9:603–20.
   Web of Science ®Google Scholar
• Collins, J. 2001. Functional estimation by assymptotic regression. Communications in Statistics: Theory and Methods 30 (12):2601–35.
   Web of Science ®Google Scholar
• Dimov, I. T. 2008. Monte Carlo methods for applied scientists. Republic of Singapore: World Scientific Publishing Co. Pte. Ltd Singapore.
   Google Scholar
• Ferrarini, A. 2011. A fitter use of Monte Carlo simulations in regression models. Computational Ecology and Software 4:240–3.
   Google Scholar
• Fishman, G. 1997. Monte-Carlo concepts algorithms and applications. Berlin: Springer-Verlag.
   Google Scholar
• Idjis, K., M. Ourbih-Tari, and L. Baghdali-Ourbih. 2017. Variance reduction in M/M/1 retrial queues using refined descriptive sampling. Communications in Statistics: Simulation and Computation. 46(6):5002–20.
   Web of Science ®Google Scholar
• Jagerman, D. L., and B. Melamed. 1992. The transition and autocorrelation structure of TES processes. Part 1: general theory. Stochastic Models 8:193–219.
   Google Scholar
• Jordi, R., and R. V. Xavier. 1996. Assessing the accuracy of analytical methods using linear regression with errors in both axes. Analytical chemistry 68 (11):1851–7.
   PubMed Web of Science ®Google Scholar
• Ourbih-Tari, M., and A. Aloui. 2009. Sampling methods and parallelism into Monte carlo simulation. Journal of Statistics: Advances in Theory and Applications 2:169–92.
   Google Scholar
• Ourbih-Tari, M., and M. Azzal. 2017. Survival function estimation with nonparametric adaptive refined descriptive sampling algorithm: A case study. Communications in Statistics: Theory and Methods 46 (12):5840–50.
   Web of Science ®Google Scholar
• Ourbih-Tari, M., A. Zioui, and A. Aloui. 2017. Variance reduction in the simulation of a stationary M/G/1 queuing system using refined descriptive sampling. Communications in Statistics: Simulation and Computation 46 (5):3504–15.
   Web of Science ®Google Scholar
• Owen, A. B. 1998. Monte Carlo, Quasi Monte Carlo, and randomized Quasi Monte Carlo. In Monte Carlo and Quasi Monte Carlo methods, ed. H. Niederreiter and J. Spanier, 86–97. Berlin, Heidelberg: Springer.
   Google Scholar
• Robert, C. P., and G. Casella. 2004. Monte Carlo statistical methods. 2nd ed. New York: Springer Science+Business Media Inc.
   Google Scholar
• Saliby, E. 1990. Descriptive sampling: A better approach to Monte Carlo simulation. Journal of the Operational Research Society 41:1133–42.
   Web of Science ®Google Scholar
• Saliby, E., and F. Pacheco. 2002. An empirical evaluation of sampling mehtods in risk analysis simulation: Quasi-Monte carlo, descriptive sampling and latin hypercube sampling. Conference Paper in Proceedings—Winter Simulation Conference 2:1606–10.
   Google Scholar
• Tari, M., and A. Dahmani. 2006. Refined descriptive sampling: A better approach to Monte Carlo simulation. Simulation Modeling Practice and Theory 14:143–60.
   Web of Science ®Google Scholar