In this article, we study the power properties of quadratic-distance-based goodness-of-fit tests. First, we introduce the concept of a <italic>root kernel</italic> and discuss the considerations that enter the selection of this kernel. We derive an easy to use normal approximation to the power of quadratic...

To construct an optimal estimating function by weighting a set of score functions, we must either know or estimate consistently the covariance matrix for the individual scores. In problems with high dimensional correlated data the estimated covariance matrix could be unreliable. The smallest...

A typical problem for the parameter estimation in normal mixture models is an unbounded likelihood and the presence of many spurious local maxima. To resolve this problem, we apply the doubly smoothed maximum likelihood estimator (DS-MLE) proposed by Seo and Lindsay (in preparation). We...