Journal of the Royal Statistical Society. Series B (Methodological)
Journal Article
Some Problems in Interval Estimation
E. C. Fieller
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 16, No. 2 (1954), pp. 175-185 (11 pages)
Published By: Wiley
https://www.jstor.org/stable/2984043
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Abstract

The object of this paper is to propose for discussion of the following topic: b1, b2, ... are unbiased estimates of β1, β2 ..., distributed normally with variances and covariances jointly estimated, with f degrees of freedom and independently of b1, b2, ..., as $v_{11}, v_{12}, v_{22}, \dots$, and the functions Fr(α) do not involve the parameters βr. What can we say about the roots of the equation in (β,α) = β1 F1 (α) + β2 F2 (α) + ... = 0? Numerical examples are discussed in detail to illustrate the problems of Ldetermining the fiducial distributions of (i) the root of a simple equation (i.e., a ratio), (ii) 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 Σ vij Fi(α) Fj(α).

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Series B (Statistical Methodology) of the Journal of the Royal Statistical Society started out simply as the Supplement to the Journal of the Royal Statistical Society in the Society's centenary year of 1934. The journal now publishes high quality papers on the methodological aspects of statistics. The objective of papers is to contribute to the understanding of statistical methodology and/or to develop and improve statistical methods. JSTOR provides a digital archive of the print version of Journal of the Royal Statistical Society, Series B: Statistical Methodology. The electronic version of Journal of the Royal Statistical Society, Series B: Statistical Methodology is available at http://www.blackwell-synergy.com/servlet/useragent?func=showIssues&code;=rssb. Authorized users may be able to access the full text articles at this site.

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Journal of the Royal Statistical Society. Series B (Methodological) © 1954 Royal Statistical Society

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