Strawderman-type estimators for a scale parameter with application to the exponential distribution

On the estimation of a normal precision and a normal variance ratio

“…Similarly, using δ 2ST in (2.3) and Theorem 3.1, we have that δ (2) ST has strictly smaller risk than (n − 4)S 2 /(m + 2)S 1 . We now show that δ (1) ST and δ (2) ST are generalized Bayes. We set η 1 = σ −2 1 and η 2 = σ −2 2 and consider the following prior distribution.…”

“…ST are as in Theorem 3.2, the term δ (2) ST /δ 0 < 1 may be interpreted as a shrinkage factor for correcting overexpansion in δ (1) ST . Likewise, the term δ (1) ST /δ 0 > 1 plays the role of an expansion factor for correcting over-shrinkage in δ (2) ST .…”

“…Let p(x) be a nonnegative and increasing function on [0,1]. If q(x) < 0 for 0 ≤ x < x 0 and q(x) > 0 for x 0 < x ≤ 1, then 1 0 p(x)q(x)dx ≥ p(x 0 ) 1 0 q(x)dx and the inequality is strict unless p(x) is a constant almost everywhere.…”

“…Suppose that b 1 (x) and b 2 (x) are densities supported on the intervals S 1 and S 2 respectively, where S 1 ⊆ S 2 and b 1 …”

“…The interest in Strawderman's [18] technique was revived by Maruyama and Strawderman [13], who used it to obtain a new class of improved generalized Bayes estimators of a very simple form for a normal variance under L 1 and also L 2 . Bobotas and Kourouklis [1] further developed Strawderman's [18] technique showing that it can be applied to estimating not only the variance of a normal distribution but also a scale parameter in a general model.…”