An estimating function approach to inference for inhomogeneous Neyman-Scott processes

This article is concerned with inference for a certain class of inhomogeneous Neyman-Scott point processes depending on spatial covariates. Regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the "mother" intensity for the Neyman-Scott process tends to infinity. Clustering parameter estimates are obtained using minimum contrast estimation based on the K-function. The approach is motivated and illustrated by applications to point pattern data from a tropical rain forest plot.     

Two-stage designs for gene-disease association studies with sample size constraints

Gene-disease association studies based on case-control designs may often be used to identify candidate polymorphisms (markers) conferring disease risk. If a large number of markers are studied, genotyping all markers on all samples is inefficient in resource utilization. Here, we propose an alternative two-stage method to identify disease-susceptibility markers. In the first stage all markers are evaluated on a fraction of the available subjects. The most promising markers are then evaluated on the remaining individuals in Stage 2. This approach can be cost effective since markers unlikely to be associated with the disease can be eliminated in the first stage. Using simulations we show that, when the markers are independent and when they are correlated, the two-stage approach provides a substantial reduction in the total number of marker evaluations for a minimal loss of power. The power of the two-stage approach is evaluated when a single marker is associated with the disease, and in the presence of multiple disease-susceptibility markers. As a general guideline, the simulations over a wide range of parametric configurations indicate that evaluating all the markers on 50% of the individuals in Stage 1 and evaluating the most promising 10% of the markers on the remaining individuals in Stage 2 provides near-optimal power while resulting in a 45% decrease in the total number of marker evaluations.     

Semiparametric model-based inference in the presence of missing responses

We consider a semiparametric model that parameterizes the conditionaldensity of the response, given covariates, but allows the marginaldistribution of the covariates to be completely arbitrary. Responsesmay be missing. A likelihood-based imputation estimator anda semi-empirical-likelihood-based estimator for the parametervector describing the conditional density are defined and provedto be asymptotically normal. Semi-empirical loglikelihood functionsfor the parameter vector and the response mean are derived.It is shown that the two semi-empirical loglikelihood functionsare distributed asymptotically as weighted ² and scaled ², respectively.