Multiparameter estimation of discrete exponential distributions

Let X₁, …, X_p be independent random variables, all having the same distribution up to a possibly varying unspecified parameter, where each of the p distributions belongs to the family of one parameter discrete exponential distributions. The problem is to estimate the unknown parameters simultaneously. Hudson (1978) shows that the minimum variance unbiased estimator (MVUE) of the parameters is inadmissible under squared error loss, and estimators better than the MVUE are proposed. Essentially, these estimators shrink the MVUE towards the origin. In this paper, we indicate that estimators shifting the MVUE towards a point different from the origin or a point determined by the observations can be obtained.     

Discriminant analysis of survey data

We consider the problem of the effect of sample designs on discriminant analysis. The selection of the learning sample is assumed to depend on the population values of auxiliary variables. Under a superpopulation model with a multivariate normal distribution, unbiasedness and consistency are examined for the conventional estimators (derived under the assumptions of simple random sampling), maximum likelihood estimators, probability-weighted estimators and conditionally unbiased estimators of parameters. Four corresponding sampled linear discriminant functions are examined. The rates of misclassification of these four discriminant functions and the effect of sample design on these four rates of misclassification are discussed. The performances of these four discriminant functions are assessed in a simulation study.     

Bayesian mixture models for complex high dimensional count data in phage display experiments

Summary.  Phage display is a biological process that is used to screen random peptide libraries for ligands that bind to a target of interest with high affinity. On the basis of a count data set from an innovative multistage phage display experiment, we propose a class of Bayesian mixture models to cluster peptide counts into three groups that exhibit different display patterns across stages. Among the three groups, the investigators are particularly interested in that with an ascending display pattern in the counts, which implies that the peptides are likely to bind to the target with strong affinity. We apply a Bayesian false discovery rate approach to identify the peptides with the strongest affinity within the group. A list of peptides is obtained, among which important ones with meaningful functions are further validated by biologists. To examine the performance of the Bayesian model, we conduct a simulation study and obtain desirable results.     

Estimation of poisson means under weighted squared error loss

In estimating the means of several independent Poisson distributions, we show that the maximum likelihood estimator is inadmissible when general weighted squared error loss is the criterion. Using this result, we extend the known results on estimation of several Poisson means (Peng 1975, Hudson 1978) to the case where possibly more than one observation is taken from each Poisson distribution and the samples are not necessarily of the same size.     

Universal domination of stein-type estimators

For the problem of estimating the location parameter of a p-variate spherically symmetric distribution (p>3), Hwang (1985) established the dominance of some positive-part James-Stein (1961) estimators over the usual estimator simultaneously under a very general class of loss function. Vie show that many of his results can be extended to a class of positive-part Baranchik-type estimators (1970).     

A Semiparametric Regression Method for Interval-Censored Data

In many medical studies, event times are recorded in an interval-censored (IC) format. For example, in numerous cancer trials, time to disease relapse is only known to have occurred between two consecutive clinic visits. Many existing modeling methods in the IC context are computationally intensive and usually require numerous assumptions that could be unrealistic or difficult to verify in practice. We propose a flexible and computationally efficient modeling strategy based on jackknife pseudo-observations (POs). The POs obtained based on nonparametric estimators of the survival function are employed as outcomes in an equivalent, yet simpler regression model that produces consistent covariate effect estimates. Hence, instead of operating in the IC context, the problem is translated into the realm of generalized linear models, where numerous options are available. Outcome transformations via appropriate link functions lead to familiar modeling contexts such as the proportional hazards and proportional odds. Moreover, the methods developed are not limited to these settings and have broader applicability. Simulations studies show that the proposed methods produce virtually unbiased covariate effect estimates, even for moderate sample sizes. An example from the International Breast Cancer Study Group (IBCSG) Trial VI further illustrates the practical advantages of this new approach.     

Efficient Stratified Testing Procedure for a False Discovery Rate

The false discovery rate (FDR) has become a popular error measure in the large-scale simultaneous testing. When data are collected from heterogenous sources and form grouped hypotheses testing, it may be beneficial to use the distinct feature of groups to conduct the multiple hypotheses testing. We propose a stratified testing procedure that uses different FDR levels according to the stratification features based on p-values. Our proposed method is easy to implement in practice. Simulations studies show that the proposed method produces more efficient testing results. The stratified testing procedure minimizes the overall false negative rate (FNR) level, while controlling the overall FDR. An example from a type II diabetes mice study further illustrates the practical advantages of this new approach.     

Estimation of the common scale of several shifted exponential distributions with unknown locations

We consider the estimation of the common scale parameter of two or more independent shifted exponential distributions with unknown locations. Under a large class of bowl-shaped loss functions, the best location-scale in-variant estimator is shown to be inadmissible. A class of improved estimators is derived. Some numerical results are presented to show the magnitude of risk reduction.     

Multiple-shrinkage estimators of means in exponential families

Shrinkage estimators are often obtained by adjusting the usual estimator towards a target subspace to which the true parameter might belong. However, meaningful reductions in risk below the usual estimator can typically be achieved in a very small part of the parameter space. In the multivariate-normal mean estimation problem, E. George, in a series of papers, showed how multiple-shrinkage estimators (data-weighted averages of several different shrinkage estimators) can attain substantial risk reductions in a large part of the parameter space. This paper extends the multiple-shrinkage results to the case of simultaneous estimation of the means of several one-parameter exponential families. Our results are developed by using an identity similar to that of Haff and Johnson (1986). A computer simulation is reported to indicate the magnitude of reductions in risk. Our results are also applied to the problem of how to choose appropriate component variables to combine before a suitable shrinkage estimator is considered.