Fitting logistic regression models is challenging when their parameters are restricted. In this article, we first develop a quadratic lower-bound (QLB) algorithm for optimization with box or linear inequality constraints and derive the fastest QLB algorithm corresponding to the smallest global...

Motivated by the likelihood functions of several incomplete categorical data, this article introduces a new family of distributions, grouped Dirichlet distributions (GDD), which includes the classical Dirichlet distribution (DD) as a special case. First, we develop distribution theory for the...

Motivated by experimental designs for drug combination studies, in this paper, we propose a novel approach for generating a uniform distribution on an arbitrary tetragon in two-dimensional Euclidean space . The key idea is to construct a one-to-one transformation between an arbitrary tetragon...

Recently, Ng et al. (2009) studied a new family of distributions, namely the nested Dirichlet distributions. This family includes the traditional Dirichlet distribution as a special member and can be adopted to analyze incomplete categorical data. However, other important aspects of the...

We consider the estimation of nonparametric regression models with the explanatory variable being measured with Berkson errors or with a mixture of Berkson and classical errors. By constructing a compact operator, the regression function is the solution of an ill-posed inverse problem, and we...

When the Newton–Raphson algorithm or the Fisher scoring algorithm does not work and the EM-type algorithms are not available, the quadratic lower-bound (QLB) algorithm may be a useful optimization tool. However, like all EM-type algorithms, the QLB algorithm may also suffer from slow...