11CONFIDENCE ESTIMATION
11.1 INTRODUCTION
In many problems of statistical inference the experimenter is interested in constructing a family of sets that contain the true (unknown) parameter value with a specified (high) probability. If X, for example, represents the length of life of a piece of equipment, the experimenter is interested in a lower bound 
for the mean θ of X. Since 
will be a function of the observations, one cannot ensure with probability 1 that 
. All that one can do is to choose a number 1 – α that is close to 1 so that 
for all θ. Problems of this type are called problems of confidence estimation. In this chapter we restrict ourselves mostly to the case where 
and consider the problem of setting confidence limits for the parameter θ.
In Section 11.2 we introduce the basic ideas of confidence estimation. Section 11.3 deals with various methods of finding confidence intervals, and Section 11.4 deals with shortest-length confidence intervals. In Section 11.5 we study ...
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