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On Robust Analysis of a Normal Location Parameter

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  • S. T. Boris Choy
  • Adrian F. M. Smith

Abstract

Pericchi and Smith considered a normal location parameter problem with double‐exponential and Student t prior distributions. These two prior distributions both belong to the class of scale mixtures of normal distributions and are useful in providing a robust analysis of the normal location parameter problem. In this paper we extend the analysis to other scale mixtures of normal distributions, such as the exponential power and the symmetric stable distributions.

Suggested Citation

  • S. T. Boris Choy & Adrian F. M. Smith, 1997. "On Robust Analysis of a Normal Location Parameter," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 463-474.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:2:p:463-474
    DOI: 10.1111/1467-9868.00079
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    Cited by:

    1. Choy, S. T. Boris & Walker, Stephen G., 2003. "The extended exponential power distribution and Bayesian robustness," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 227-232, November.
    2. Kevin McNally, 2023. "How Valuable Are Small Measurement Datasets in Supplementing Occupational Exposure Models? A Numerical Study Using the Advanced Reach Tool," IJERPH, MDPI, vol. 20(7), pages 1-14, April.
    3. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    4. Guo, Wen-Chung & Lai, Fu-Chuan, 2024. "R&D investments and location choices with three firms," International Review of Economics & Finance, Elsevier, vol. 92(C), pages 1448-1459.
    5. Stephen Walker, 1999. "The uniform power distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 509-517.
    6. Zhou, Yanju & Che, Yuan, 2021. "Research on Government Logistics Subsidies for Poverty Alleviation with Non-uniform Distribution of Consumers," Omega, Elsevier, vol. 104(C).
    7. Dragone, Davide & Lambertini, Luca, 2020. "Equilibrium existence in the Hotelling model with convex production costs," Regional Science and Urban Economics, Elsevier, vol. 84(C).
    8. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.
    9. Dyskeland, Ole Kristian & Foros, Øystein, 2023. "Multihoming and market expansion: Effects on media platforms’ pricing and content creation incentives," Economics Letters, Elsevier, vol. 232(C).
    10. Ronen Gradwohl & Moshe Tennenholtz, 2022. "Pareto-Improving Data-Sharing," Papers 2205.11295, arXiv.org.
    11. Giles Hooker & Anand Vidyashankar, 2014. "Bayesian model robustness via disparities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 556-584, September.
    12. Giuseppe De Luca & Jan R. Magnus & Franco Peracchi, 2021. "Posterior moments and quantiles for the normal location model with Laplace prior," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(17), pages 4039-4049, August.
    13. Giuseppe De Luca & Jan Magnus & Franco Peracchi, 2022. "Asymptotic properties of the weighted average least squares (WALS) estimator," Tinbergen Institute Discussion Papers 22-022/III, Tinbergen Institute.
    14. Baker, Matthew J. & George, Lisa M., 2024. "The news hour: Welfare estimation in the market for local television news," International Journal of Industrial Organization, Elsevier, vol. 94(C).
    15. Hong Feng & Jie Ma, 2018. "Location choices and third‐degree spatial price discrimination," Scottish Journal of Political Economy, Scottish Economic Society, vol. 65(2), pages 142-153, May.
    16. John S. Heywood & Dongyang Li & Guangliang Ye, 2022. "Mixed duopoly under hotelling with convex production costs," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 69(2), pages 487-510, October.
    17. Kim, SungBum & Kim, Hyoung-Moon, 2022. "Series form of the characteristic functions of scale mixtures of multivariate skew-normal distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 172-187.
    18. Kim, Hyoung-Moon, 2008. "A note on scale mixtures of skew normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1694-1701, September.
    19. Kim, Hyoung-Moon & Ryu, Duchwan & Mallick, Bani K. & Genton, Marc G., 2014. "Mixtures of skewed Kalman filters," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 228-251.

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