381
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Bayesian inference using least median of squares and least trimmed squares in models with independent or correlated errors and outliers

Pages 5761-5772 | Received 30 Jun 2022, Accepted 29 Jun 2023, Published online: 16 Jul 2023

References

  • Bissiri, P. G., C. C. Holmes, and S. G. Walker. 2016. A general framework for updating belief distributions. Journal of the Royal Statistical Society. Series B, Statistical Methodology 78 (5):1103–30. doi: 10.1111/rssb.12158.
  • Chernozhukov, V., and H. Hong. 2003. An MCMC approach to classical estimation. Journal of Econometrics 115 (03):100–3. doi: 10.1016/S0304-4076(03)00100-3.
  • DiCiccio, T. J., R. E. Kass, A. Raftery, and L. Wasserman. 1997. Computing Bayes factors by combining simulation and asymptotic approximations. Journal of the American Statistical Association 92 (439):903–15. doi: 10.2307/2965554.
  • Geweke, J. 1992. Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In Bayesian statistics, ed. J. M. Bernado, J. O. Berger, A. P. Dawid and A. F. M. Smith, vol. 4, 169–93. Oxford, UK: Clarendon Press.
  • Hastings, W. K. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 (1):97–109. doi: 10.2307/2334940.
  • Kato, K. 2013. Quasi-Bayesian analysis of nonparametric instrumental variables models. The Annals of Statistics 41 (5), 2359–90. doi: 10.1214/13-AOS1150.
  • Matusita, K. 1953. On the estimation by the minimum distance method. Annals of the Institute of Statistical Mathematics 5 (2):59–65. doi: 10.1007/BF02949801.
  • Matusita, K. 1955. Decision rules, based on the distance, for problems of fit, two samples, and estimation. The Annals of Mathematical Statistics 26 (4):631–40. doi: 10.1214/aoms/1177728422.
  • Matusita, K. 1964. Distance and decision rules. Annals of the Institute of Statistical Mathematics 16 (1):305–15. doi: 10.1007/BF02868578.
  • Piradl, S., A. Shadrokh, and M. Yarmohammadi. 2021. A robust estimation method for the linear regression model parameters with correlated error terms and outliers. Journal of Applied Statistics 49 (7):1663–76. doi: 10.1080/02664763.2021.1881454.
  • Raj, S., and K. K. Senthamarai. 2017. Detection of outliers in regression model for medical data. International Journal of Medical Research & Health Sciences 6 (7):2319–5886.
  • Rousseeuw, P. J. 1984. Least median of squares regression. Journal of the American Statistical Association 79 (388):871–80. doi: 10.2307/2288718.
  • Tierney, L. 1994. Markov chains for exploring posterior distributions. Annals of Statistics 22:1701–62. https://www.jstor.org/stable/2242477.