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Confidence intervals for the normal mean utilizing prior information

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  • Farchione, David
  • Kabaila, Paul

Abstract

Consider X1,X2,...,Xn that are independent and identically N([mu],[sigma]2) distributed. Suppose that we have uncertain prior information that [mu]=0. We answer the question: To what extent can a frequentist 1-[alpha] confidence interval for [mu] utilize this prior information?

Suggested Citation

  • Farchione, David & Kabaila, Paul, 2008. "Confidence intervals for the normal mean utilizing prior information," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1094-1100, July.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:9:p:1094-1100
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    References listed on IDEAS

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    1. Kabaila, Paul, 1998. "Valid Confidence Intervals In Regression After Variable Selection," Econometric Theory, Cambridge University Press, vol. 14(4), pages 463-482, August.
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    1. Kabaila, Paul, 2011. "Admissibility of the usual confidence interval for the normal mean," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 352-359, March.
    2. Farchione, Davide & Kabaila, Paul, 2012. "Confidence intervals in regression centred on the SCAD estimator," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1953-1960.
    3. Paul Kabaila & Nishika Ranathunga, 2021. "Computation of the expected value of a function of a chi-distributed random variable," Computational Statistics, Springer, vol. 36(1), pages 313-332, March.
    4. Kabaila, Paul, 2013. "Note on a paradox in decision-theoretic interval estimation," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 123-126.
    5. Paul Kabaila, 2009. "The Coverage Properties of Confidence Regions After Model Selection," International Statistical Review, International Statistical Institute, vol. 77(3), pages 405-414, December.
    6. Kabaila, Paul & Giri, Khageswor, 2009. "Large-sample confidence intervals for the treatment difference in a two-period crossover trial, utilizing prior information," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 652-658, March.

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