Wen-Tao Huang

Bayesian Sampling Plans for Exponential Distribution Based on Type I Censoring Data

We study variable sampling plans for the exponential distribution based on type I censoring data. Using a suitable loss function, a Bayesian variable sampling plan (nB, tB, δB) is derived. For certain prior distributions and loss functions, the numerical values of the Bayesian sampling plans and the associated minimum Bayes risks are tabulated. In terms of Bayes risks, comparisons between the proposed Bayesian sampling plans (nB, tB, δB) and the “Bayesian” variable sampling plans (n0, t0, δLT0) of Lam (1994, Ann. Statist., 22, 696–711) have been made. The numerical results indicate that under the same conditions, the proposed Bayesian sampling plan is superior to that of Lam in the sense that the Bayes risk of (nB, tB, δB) is less than that of (n0, t0, δLT0).

Covariate-Adjusted Adaptive Designs for Continuous Responses in a Phase III Clinical Trial: Recommendation for Practice

ABSTRACT One adaptive design is proposed and studied by Bandyopadhyay and Biswas (2001) for comparing two treatments having continuous responses with covariates at hand in a phase III clinical trial. On the other hand, a drop-the-loser urn design is recently proposed by Ivanova (2003), which is known to have the least variability among urn-based adaptive designs for binary responses. The drop-the-loser rule for continuous data was recently introduced by Ivanova et al. (2006). But neither of the works considered covariates for the allocation design. The present paper provides a version of the newly proposed adaptive design, drop-the-loser rule, but for continuous responses and by incorporating the covariate information in the allocation procedure. Several exact and limiting properties of the design, and also of a simpler version of it, are studied. We compare the design of Bandyopadhyay and Biswas (2001) with the covariate-adjusted drop-the-loser-type rule for continuous responses and conclude that, although the drop-the-loser rule is better for binary responses, the design of Bandyopadhyay and Biswas (2001) performs better than the drop-the-loser-type rule for continuous responses with covariates. We recommend the existing design of Bandyopadhyay and Biswas (2001) for practical purposes.

Goodness-of-fit testing in growth curve models: A general approach based on finite differences

Growth curve models are routinely used in various fields such as biology, ecology, demography, population dynamics, finance, econometrics, etc. to study the growth pattern of different populations and the variables linked with them. Many different kinds of growth patterns have been used in the literature to model the different types of realistic growth mechanisms. It is generally a matter of substantial benefit to the data analyst to have a reasonable idea of the nature of the growth pattern under study. As a result, goodness-of-fit tests for standard growth models are often of considerable practical value. In this paper we develop some natural goodness-of-fit tests based on finite differences of the size variables under consideration. The method is general in that it is not limited to specific parametric forms underlying the hypothesized model so long as an appropriate finite difference of some function of the size variables can be made to vanish. In addition it allows the testing process to be carried out under a set up which manages to relax most of the assumptions made by Bhattacharya et al. (2009); these assumptions are generally reasonable but not guaranteed to hold universally. Thus our proposed method has a very wide scope of application. The performance of the theory developed is illustrated numerically through several sets of real data and through simulations.

Generalized subset selection procedures under heteroscedasticity

Abstract In this paper, we propose and study a generalized subset selection procedure for selecting the best population. Based on the concept of generalized subset selection procedure, some selection procedures for normal populations are proposed and studied. They are used, respectively, to select the best population (populations) with respect to the largest mean, the largest p th quantile and the largest signal-to-noise ratio. For the case of common unknown variance, the proposed generalized subset selection procedure for selecting the largest mean becomes exactly the same as that has been given in Hsu (in: T.J. Santner, A.C. Tamhane (Eds.), Design of Experiments: Ranking and Selection, Marcel Dekker, New York, 1984, pp. 179–198). A Monte Carlo study shows that the proposed generalized subset selection procedures behave satisfactorily. An illustration of a set of real data is also given.