Evaluación de rendimiento de los estimadores para los parámetros de la Distribución Burr XII
Performance Evaluation of Estimators for the Burr XII Distribution Parameters
Resumen (es)
Este trabajo tiene como objetivo principal evaluar el rendimiento de los estimadores de máxima verosimilitud y estimadores puntuales bayesianos para los parámetros p e b de la distribución Burr XII y sus versiones corregidas por bootstrap. Simulaciones de Monte Carlo fueron utilizadas para el análisis, considerando diversos escenarios y verificando algunas propiedades de esos estimadores, como la media, varianza, sesgo y error cuadrático medio. Los estimadores corregidos presentaron mejores rendimientos en cuanto a la estimación por el método de máxima verosimilitud, no sucede lo mismo en las estimativas puntuales para el análisis de los estimadores bayesianos.
Resumen (en)
The main objective of this paper is to evaluate the performance of maximum likelihood estimators and Bayesian point estimators for the parameters p and b of the Burr XII distribution and its bootstrap-corrected versions. Monte Carlo simulations were used for the analysis, considering various scenarios and verifying some properties of these estimators, such as the mean, variance, bias, and mean squared error. The corrected estimators presented better performances in terms of the estimation by the maximum likelihood method, the same does not happen in the point estimates for the analysis of the Bayesian estimators.
Referencias
A. Bovas and A. Thavaneswaran. A nonlinear time series model and estimation of missing data. Annals of the Institute of Statistical Mathematics, 43(3):493–504, September 1991.
I. W. Burr. Cumulative frequency functions. The Annals of mathematical statistics, 13(2):215–232, 1942.
S. Calderon and F. Nieto. Bayesian analysis of Multivariate Threshold Autoregressive Models with Missing Data. Communications in Statistics: Theory and Methods, 46(1):296–318, 2017.
B. P. Carlin and S. Chib. Bayesian Model Choice via Markov Chain Monte Carlo Methods. Journal of the Royal Statistical Society. Series B (Methodological), 57(3):473–484, September 1995.
B. P. Carlin, N. G. Polson, and D. S. Stoffer. A Monte Carlo approach to Nonnormal and Nonlinear State-Space Modeling. Journal of the American Statistical Association, 87(418):473–484, June 1992.
C. Carter and R. Konh. On Gibbs Sampling for State Space Models. Biometrika, 81(3):541–553, August 1994.
C. Chen and J. Lee. Bayesian inference of threshold autoregressive models. Journal of Time Series Analysis, 16(5):483–492, September 1995.
C. W. S. Chen, F. Liu, and R. Gerlach. Bayesian subset selection for threshold autoregressive moving-average models. Computational Statistics, 26(1):1–30, 2011.
S. Chib. Marginal Likelihood from the Gibbs Output. Journal of the American Statistical Association, 90(432):1313–1321, December 1995.
S. Chib and I. Jeliazkov. Marginal Likelihood from the Metropolis-Hastings Output. Journal of the American Statistical Association, 96(453):270–281, March 2001.
J. G. De Gooijer and A. Vidiella-i Anguera. Forecasting threshold cointegrated systems. International Journal of Forecasting, 20(2):237–253, 2004.
P. Dellaportas, J. Forster, and I. Ntzoufras. On Bayesian model and variable selection using MCMC. Statistics and Computing, 12(1):27–36, 2002.
B. Efron. Bootstrap methods: Another look at the jackknife. The Annals of Statistics, pages 1–26, 1979.
B. Efron and R. J. Tibshirani. An introduction to the bootstrap chapman & hall. New York, 436, 1993.
S. Frh¨uwirth-Schnatter. Data augmentation and dynamic linear models. Journal of Time Series Analysis, 15(2):183–202, March 1995.
D. Gamerman and H. F. Lopes. Markov chain Monte Carlo: stochastic simulation for Bayesian inference. CRC Press, 2006.
E. George and R. McCulloch. Variable Selection Via Gibbs Sampling. Journal of the American Statistical Association, 8(423):881–889, September 1993.
P. Green. Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination. Biometrika, 82(4):711–732, December 1995.
B. Hansen. Threshold autoregression in economics. Statistics and Its Interface, 4(2):123–127, 2011.
A. Harvey. Forecasting, structural time series model and the Kalman filter. Cambridge University Press, Cambridge, 1989. ISBN 0-521-32196-4.
T. Hong and T. Lee. Diagnostic Checking for the Adequacy of Nonlinear Time Series Models. Econometric Theory, 19(6):1065–1121, December 2003.
L. Kuo and B. Mallick. Variable Selection for Regression Models. Sankhya: The Indian Journal of Statistics, Series B, 60(1):65–81, April 1998.
Y. Kwon. Bayesian Analysis of Threshold Autoregressive Models. PhD thesis, University of Tennessee - Knoxville, 2003.
Y. Kwon, H. Bozdogan, and H. Bensmail. Performance of Model Selection Criteria in Bayesian Threshold VAR (TVAR) Models. Econometric Reviews, 28(1-3):83–101, December 2009.
S. Ling and W. Li. Diagnostic checking of nonlinear multivariate time series with multivariate arch errors. Journal of Time Series Analysis., 18(5):447–464, September 1997.
J. G. MacKinnon and A. A. Smith Jr. Approximate bias correction in econometrics. Journal of Econometrics, 85(2):205–230, 1998.
S. Meyn and R. Tweedie. Markov Chains and Stochastic Stability. Oxford Statistical Science. CAMBRIDGE UNIVERSITY PRESS, Cambridge, 2009. ISBN 978-0-511-51671-9.
D. Moore and A. S. Papadopoulos. The burr type xii distribution as a failure model under various loss functions. Microelectronics Reliability, 40(12):2117–2122, 2000.
F. Nieto. Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics - Theory and Methods., 34(4):905–930, February 2005.
Cómo citar
Licencia
Los autores mantienen los derechos sobre los artículos y por tanto son libres de compartir, copiar, distribuir, ejecutar y comunicar públicamente la obra bajo las condiciones siguientes:
Reconocer los créditos de la obra de la manera especificada por el autor o el licenciante (pero no de una manera que sugiera que tiene su apoyo o que apoyan el uso que hace de su obra).
Comunicaciones en Estadística está bajo una licencia Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0)
