In this paper we propose James–Stein type estimators for variances raised to a fixed power by shrinking individual variance estimators towards the arithmetic mean. We derive and estimate the optimal choices of shrinkage parameters under both the squared and the Stein loss functions. Asymptotic...

Microarrays are one of the most widely used high throughput technologies. One of the main problems in the area is that conventional estimates of the variances that are required in the "t"-statistic and other statistics are unreliable owing to the small number of replications. Various methods...

It has been noticed by several authors that there is a small but non-zero probability that the GCV estimate [lambda] of the smoothing parameter in spline and related smoothing problems will be extremely small, leading to gross undersmoothing. We obtain an upper bound to the probability that the...

Bayesian confidence intervals of a smoothing spline are often used to distinguish two curves. In this paper, we provide an asymptotic formula for sample-size calculations based on Bayesian confidence intervals. Approximations and simulations on special functions indicate that this asymptotic...