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Some Problems in Interval Estimation
Abstract
Summary: The object of this paper is to propose for discussion the following topic: b1, b2, … are unbiased estimates of β1, β2, …, distributed normally with variances and covariances jointly estimated, with / degrees of freedom and independently of b1, b2, …, as v11, v12, v22, …, and the functions Fr(α) do not involve the parameters βr. What can we say about the roots of the equation in F(β,α)=β1F1(α)+β2 F2(α)+…=0? Numerical examples are discussed in detail to illustrate the problems of determining the fiducial distributions of (i)the root of a simple equation (i.e., a ratio),(i)the roots of a quadratic equation with variable coefficients. The solutions proposed are based on a consideration of the region of the (α, t2) plane lying above the curve {F(b,α)}2=t2 V{F(b,α)}=t2∑vijFi(α)Fj(α).
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Citations
Cited by
Efron, B., & Tibshirani, R. (1986) · Statistical Science · doi:10.1214/ss/1177013815 · Cited by 6,033
Causal Inference Using Potential Outcomes: Design, Modeling, Decisions
Rubin, D. B. (2005) · Journal of the American Statistical Association · doi:10.1198/016214504000001880 · Cited by 2,173
Cowling, B. J., Ali, S. T., Ng, T. W. Y., Tsang, T. K., Li, J. C. M., Fong, M. W., Liao, Q., Kwan, M. Y., Lee, S. L., Chiu, S. S., et al. (2020) · The Lancet Public Health · doi:10.1016/s2468-2667(20)30090-6 · Cited by 1,258
Ramsey, S. D., Willke, R. J., Glick, H., Reed, S. D., Augustovski, F., Jonsson, B., Briggs, A., & Sullivan, S. D. (2015) · Value in Health · doi:10.1016/j.jval.2015.02.001 · Cited by 811
Hróbjartsson, A., Thomsen, A. S. S., Emanuelsson, F., Tendal, B., Hilden, J., Boutron, I., Ravaud, P., & Brorson, S. (2013) · Canadian Medical Association Journal · doi:10.1503/cmaj.120744 · Cited by 527
Metadata
- Authors
- Fieller, E. C.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1954-07-01
- Volume
- 16
- Issue
- 2
- Pages
- 175-185
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2527882685
- Cited by
- 1,139
- References
- 0
- FWCI
- 4.52
- Type
- journal article
- Language
- en
- Open access
- closed
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- Fieller, E. C. (1954). Some Problems in Interval Estimation. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1954.tb00159.x
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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