A comparison of methods for estimating parameters of the stochastic Lomax process: through simulation study
Öz
In this paper, we study the problem of parameter estimation of the stochastic Lomax diffusion process, this process was introduced in [A. Nafidi, I. Makroz, and R. Gutiérrez Sánchez, A stochastic lomax diffusion process: Statistical inference and application, Mathematics, 2021][14], and the authors suggested the method of simulated annealing to find the maximum likelihood estimators of this process. In this work, we propose alternative methods for finding the maximum likelihood estimators, namely Genetic algorithm and Nelder-Mead, we also investigate the use of Markov Chain Monte Carlo method to determine the model parameters. Finally, an example of application through the simulation of paths for the process is suggested. Then, a comparison is made between the application of three algorithms based on their accuracy and time of execution.
Anahtar Kelimeler
Lomax diffusion process trend analysis metaheuristic optimization algorithms Markov Chain Monte Carlo simulation likelihood estimation
Kaynakça
- [1] Y. Aït-Sahalia, Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach, Econometrica 70 (1), 223-262, 2002.
- [2] F.M. Bandi and P.C. Phillips, Fully nonparametric estimation of scalar diffusion models, Econometrica 71 (1), 241-283, 2003.
- [3] A. Beskos, O. Papaspiliopoulos, G.O. Roberts and P. Fearnhead, Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion), J R Stat Soc Series B Stat Methodol 68 (3), 33-382, 2006.
- [4] J. Fan, A selective overview of nonparametric methods in financial econometrics, Stat Sci 20 (4), 317-337, 2005.
- [5] D. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, 1989.
- [6] A. Golightly and D.J. Wilkinson, Bayesian inference for nonlinear multivariate diffusion models observed with error, Comput Stat Data Anal 52 (3), 1674-1693, 2008.
- [7] R. Gutiérrez, R. Gutiérrez-Sánchez, A. Nafidi and E. Ramos, Three-parameter stochastic lognormal diffusion model: statistical computation and simulating annealingapplication to real case, J. Stat. Comput. Simul. 79 (1), 25-38, 2009.
- [8] A.S. Hurn and K. Lindsay, Estimating the parameters of stochastic differential equations, Math Comput Simul 48 (4-6), 373-384, 1999.
- [9] G.J. Jiang and J.L. Knight, A nonparametric approach to the estimation of diffusion processes, with an application to a short-term interest rate model, Econ Theory 13 (5), 615-645, 1997.
- [10] J.C. Lagarias, J.A. Reeds, M.H. Wright and P.E. Wright, Convergence properties of the neldermead simplex method in low dimensions, SIAM J. Optim. 9 (1), 112-147, 1998.
- [11] C. Li, Maximum-likelihood estimation for diffusion processes via closed-form density expansions, Ann. Stat. 41 (3), 1350-1380, 2013.
- [12] A. Nafidi, M. Bahij, B. Achchab and R. Gutiérrez-Sánchez, The stochastic Weibull diffusion process: Computational aspects and simulation, Appl. Math. Comput. 348, 575-587, 2019.
- [13] A. Nafidi and A. El Azri, A stochastic diffusion process based on the lundqvistkorf growth: Computational aspects and simulation, Math Comput Simul 182, 25-38, 2021.
- [14] A. Nafidi, I. Makroz and R. Gutiérrez Sánchez, A stochastic lomax diffusion process: Statistical inference and application, Mathematics 9 (1), 100, 2021.
- [15] M. Plummer, N. Best, K. Cowles and K. Vines,Coda: convergence diagnosis and output analysis for mcmc, R News 6 (1), 711, 2006.
- [16] M. Plummer, A. Stukalov, M. Denwood and M.M. Plummer, R Package "rjags", Vienna, Austria, 2016.
- [17] P. Román-Román, D. Romero, M. Rubio and F. Torres-Ruiz, Estimating the parameters of a gompertz-type diffusion process by means of simulated annealing, Appl. Math. Comput. 218 (9), 5121-5131, 2012.
- [18] P. Román-Román and F. Torres-Ruiz, A stochastic model related to the richards-type growth curve. estimation by means of simulated annealing and variable neighborhood search, Appl. Math. Comput. 266, 579-598, 2015.
- [19] O. Stramer and M. Bognar, Bayesian inference for irreducible diffusion processes using the pseudo-marginal approach, Bayesian Anal. 6 (2), 231-258, 2011.
- [20] D. Whitley, A genetic algorithm tutorial, Stat Comput 4 (2), 65-85, 1994.
Öz
Kaynakça
- [1] Y. Aït-Sahalia, Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach, Econometrica 70 (1), 223-262, 2002.
- [2] F.M. Bandi and P.C. Phillips, Fully nonparametric estimation of scalar diffusion models, Econometrica 71 (1), 241-283, 2003.
- [3] A. Beskos, O. Papaspiliopoulos, G.O. Roberts and P. Fearnhead, Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion), J R Stat Soc Series B Stat Methodol 68 (3), 33-382, 2006.
- [4] J. Fan, A selective overview of nonparametric methods in financial econometrics, Stat Sci 20 (4), 317-337, 2005.
- [5] D. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, 1989.
- [6] A. Golightly and D.J. Wilkinson, Bayesian inference for nonlinear multivariate diffusion models observed with error, Comput Stat Data Anal 52 (3), 1674-1693, 2008.
- [7] R. Gutiérrez, R. Gutiérrez-Sánchez, A. Nafidi and E. Ramos, Three-parameter stochastic lognormal diffusion model: statistical computation and simulating annealingapplication to real case, J. Stat. Comput. Simul. 79 (1), 25-38, 2009.
- [8] A.S. Hurn and K. Lindsay, Estimating the parameters of stochastic differential equations, Math Comput Simul 48 (4-6), 373-384, 1999.
- [9] G.J. Jiang and J.L. Knight, A nonparametric approach to the estimation of diffusion processes, with an application to a short-term interest rate model, Econ Theory 13 (5), 615-645, 1997.
- [10] J.C. Lagarias, J.A. Reeds, M.H. Wright and P.E. Wright, Convergence properties of the neldermead simplex method in low dimensions, SIAM J. Optim. 9 (1), 112-147, 1998.
- [11] C. Li, Maximum-likelihood estimation for diffusion processes via closed-form density expansions, Ann. Stat. 41 (3), 1350-1380, 2013.
- [12] A. Nafidi, M. Bahij, B. Achchab and R. Gutiérrez-Sánchez, The stochastic Weibull diffusion process: Computational aspects and simulation, Appl. Math. Comput. 348, 575-587, 2019.
- [13] A. Nafidi and A. El Azri, A stochastic diffusion process based on the lundqvistkorf growth: Computational aspects and simulation, Math Comput Simul 182, 25-38, 2021.
- [14] A. Nafidi, I. Makroz and R. Gutiérrez Sánchez, A stochastic lomax diffusion process: Statistical inference and application, Mathematics 9 (1), 100, 2021.
- [15] M. Plummer, N. Best, K. Cowles and K. Vines,Coda: convergence diagnosis and output analysis for mcmc, R News 6 (1), 711, 2006.
- [16] M. Plummer, A. Stukalov, M. Denwood and M.M. Plummer, R Package "rjags", Vienna, Austria, 2016.
- [17] P. Román-Román, D. Romero, M. Rubio and F. Torres-Ruiz, Estimating the parameters of a gompertz-type diffusion process by means of simulated annealing, Appl. Math. Comput. 218 (9), 5121-5131, 2012.
- [18] P. Román-Román and F. Torres-Ruiz, A stochastic model related to the richards-type growth curve. estimation by means of simulated annealing and variable neighborhood search, Appl. Math. Comput. 266, 579-598, 2015.
- [19] O. Stramer and M. Bognar, Bayesian inference for irreducible diffusion processes using the pseudo-marginal approach, Bayesian Anal. 6 (2), 231-258, 2011.
- [20] D. Whitley, A genetic algorithm tutorial, Stat Comput 4 (2), 65-85, 1994.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Hesaplamalı İstatistik, Olasılık Teorisi, Uygulamalı İstatistik, İstatistik (Diğer) |
| Bölüm | İstatistik |
| Yazarlar | |
| Erken Görünüm Tarihi | 2 Mart 2024 |
| Yayımlanma Tarihi | 23 Nisan 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 53 Sayı: 2 |