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Confidence Intervals

Chapter
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Part of the Springer Texts in Statistics book series (STS)

Abstract

We discussed interval estimation briefly in Chapters 3 and 4. We shall recall briefly how interval estimation differs from the considerations of Chapters 5 and 7, in which D consisted of the possible values of some function ϕ of the unknown parameter value θ, the decision d0 meaning “my guess is that the true value of ϕ(θ) is d0.” Thus d0 was typically a single point of an interval D (i.e., for simplicity we think of the set of decisions as a real number interval), and these problems were termed ones of point estimation. If the decision is to be an interval of real numbers rather than a single point, the problem is called one of interval estimation. In a problem of this kind, a decision may be “my guess is that the table is between 4 and 4.3 feet long” rather than “my guess is that the table is 4.1 feet long.” Thus, if were discussing confidence intervals, D consists of a collection of intervals, and we may denote by [a, b] that decision which consists of the set of real numbers between a and b inclusive; the decision in the example of the table would be [4.0,4.3].

Keywords

Loss Function Coverage Probability Interval Estimation Confidence Coefficient Real Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag New York Inc. 1987

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