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Confidence Distribution and Distribution Estimation for Modern Statistical Inference

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Springer Handbook of Engineering Statistics

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Abstract

This chapter introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of the statistical inference methodology and to utilize distribution estimators in practice. We also include in the discussion the topic of generalized fiducial inference, a special type of modern distributional inference, and relate it to the concept of confidence distribution. Several real data examples are also provided for practitioners. We hope that the selected content covers the greater part of the developments on this subject.

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Notes

  1. 1.

    In (ii) the sum spans over \(\binom np\) of p-tuples of indexes i = (1 ≤ i1 < ⋯ < ip ≤ n). For any n × p matrix A, the sub-matrix (A)i is the p × p matrix containing the rows i = (i1, …, ip) of A.

  2. 2.

    ψ(x) is the digamma function defined by \(\psi (z)=\frac {d}{dz}\log (\Gamma (z))\) for z > 0, where Γ is gamma function.

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  1. Zhejiang University, Hangzhou, Zhejiang, China

    Yifan Cui

  2. Rutgers University, New Brunswick, NJ, USA

    Min-ge Xie

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  1. Department of Industrial & Systems Engineering, Rutgers University, Piscataway, NJ, USA

    Hoang Pham

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    Cui, Y., Xie, Mg. (2023). Confidence Distribution and Distribution Estimation for Modern Statistical Inference. In: Pham, H. (eds) Springer Handbook of Engineering Statistics. Springer Handbooks. Springer, London. https://doi.org/10.1007/978-1-4471-7503-2_29

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