A recently developed penalized non-parametric maximum likehood estimate (NPMLE), of a non-increasing density, overcomes the so-called spiking problem in the well-known NPMLE. In this paper, some iterative procedures for choosing the optimal smoothing parameter in the penalized NPMLE are...

A semiparametric mixture model is characterized by a non-parametric mixing distribution <b><scriptface>Q</scriptface></b> (with respect to a parameter <b>"θ"</b>) and a structural parameter <b>"β"</b> common to all components. Much of the literature on mixture models has focused on fixing <b>"β"</b> and estimating <scriptface>Q</scriptface>. However, this can lead to...

When thousands of tests are performed simultaneously to detect differentially expressed genes in microarray analysis, the number of Type I errors can be immense if a multiplicity adjustment is not made. However, due to the large scale, traditional adjustment methods require very stringen...