Exact Evaluation of Two-Stage Stein-Like Procedures – Review

Abstract

The present article reviews several published papers in which the distributions of stopping variables, the expected values, risk functions, and coverage probabilities of estimators at stopping were derived analytically for two-stage Stein-like procedures. The reviewed papers deal with fixed-width and bounded risk estimation of the location and scale parameters of exponential distributions; the fixed-width interval estimation of the log-odds in Bernoulli trials; fixed-width interval estimation of the common variance of equicorrelated normal distributions; and estimating the difference of two normal means when the ratio of variances is known. The estimation of the scale parameter of a gamma distribution for arbitrary known shape parameter is also discussed.

Keywords:

• Bernoulli trials
• Bounded risk
• Common variance
• Coverage probability
• Equi-correlated
• Exact evaluation
• Fixed-width
• Interval estimator
• Two-stage sampling

Subject Classifications:

• Primary: 62L12
• Secondary: 60G40