Accuracy functions for confidence bounds: a basis for sample size determination
In many applications of statistics, a one-sided confidence bound provides the desired form of inference. In designing experiments or choosing data to be collected for such applications, there is no standard basis currently offered in the literature for determining sample sizes. This thesis attempts to provide such a basis. Suppose X is a random vector with distribution P/sub theta, nu/, where theta is a real parameter and the parameter of interest and nu is a nuisance parameter. Suppose theta(X) and anti theta(X) are, respectively, (1-..cap alpha..)-lower and -upper confidence bounds for theta. The absolute accuracy functions for the lower and upper confidence bounds are defined, respectively, by P/sub theta, nu/ (anti theta-c 0; and relative accuracy functions, by P/sub theta, nu/(theta-c theta < theta (X)) for c belongs to (0,1) and theta > 0 and P/sub anti theta, nu/(theta (X) < theta + ctheta) for c > 0 and theta > 0. It is proposed that the size of a sample on which a confidence bound is to be computed may, in many instances, be appropriately based on the criterion that a selected accuracy function be at least of size ..beta.. where ..beta.. belongs to (..cap alpha..,1). In some applications, it is possible to find a sample size satisfying the selected criterion for all possible values of theta and nu; in others, it is possible to satisfy it only for a restricted range of values. The accuracy functions are investigated in several settings. In the one- and two-sample location and scale problem, the accuracy functions are found to be constant or monotonic under natural invariance assumptions on the confidence bounds.
- Research Organization:
- California Univ., Berkeley (USA)
- OSTI ID:
- 5663079
- Country of Publication:
- United States
- Language:
- English
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