Some multiple comparison procedures for comparing treatments within several groups

Multiple comparison procedures are extended to designs consisting of several groups, where the treatment means are to be compared within each group. This may arise in two-factor experiments, with a significant interaction term, when one is interested in comparing the levels of one factor at each level of the other factor. A general approach is presented for deriving the distributions and calculating critical points, following three papers which dealt with two specific procedures. These points are used for constructing simultaneous confidence intervals over some restricted set of contrasts among treatment means in each of the groups. Tables of critical values are provided for two procedures and an application is demonstrated. Some extensions are presented for the case of possible different sets of contrasts and also for unequal variances in the various groups.     

On the almost unbiased generalized liu estimator and unbiased estimation of the bias and mse

In this paper, we derive the almost unbiased generalized Liu estimator and examine an exact unbiased estimator of the bias and mean squared error of the feasible generalized Liu estimator . We compare the almost unbiased generalized Liu estimator (AUGLE) with the generalized Liu estimator (GLE) and with the ordinary least squares estimator (OLSE).     

Inflated modified power series distributions with applications

In certain applications involving discrete data, it is sometimes found that X = 0 is observed with a frequency significantly higher than predicted by the assumed model. Zero inflated Poisson, binomial and negative binomial models have been employed in some clinical trials and in some regression analysis problems.

In this paper, we study the zero inflated modified power series distributions (IMPSD) which include among others the generalized Poisson and the generalized negative binomial distributions and hence the Poisson, binomial and negative binomial distributions. The structural properties along with the distribution of the sum of independent IMPSD variables are studied. The maximum likelihood estimation of the parameters of the model is examined and the variance-covariance matrix of the estimators is obtained. Finally, examples are presented for the generalized Poisson distribution to illustrate the results.     

P-value adjustment for multiple binary endpoints

The p-value-based adjustment of individual endpoints and the global test for an overall inference are the two general approaches for the analysis of multiple endpoints. Statistical procedures developed for testing multivariate outcomes often assume that the multivariate endpoints are either independent or normally distributed. This paper presents a general approach for the analysis of multivariate binary data under the framework of generalized linear models. The generalized estimating equations (GEE) approach is applied to estimate the correlation matrix of the test statistics using the identity and exchangeable working correlation matrices with the model-based as well as robust estimators. The objectives of the approaches are the adjustment of p-values of individual endpoints to identify the affected endpoints as well as the global test of an overall effect. A Monte Carlo simulation was conducted to evaluate the overall family wise error (FWE) rates of the single-step down p-value adjustment approach from two adjustment methods to three global test statistics. The p-value adjustment approach seems to control the FWE better than the global approach Applications of the proposed methods are illustrated by analyzing a carcinogenicity experiment designed to study the dose response trend for 10 tumor sites, and a developmental toxicity experiment with three malformation types: external, visceral, and skeletal.     

Likelihood-based cross-validation score for selecting the smoothing parameter in maximum penalized likelihood estimation

Maximum penalized likelihood estimation is applied in non(semi)-para-metric regression problems, and enables us exploratory identification and diagnostics of nonlinear regression relationships. The smoothing parameter A controls trade-off between the smoothness and the goodness-of-fit of a function. The method of cross-validation is used for selecting A, but the generalized cross-validation, which is based on the squared error criterion, shows bad be¬havior in non-normal distribution and can not often select reasonable A. The purpose of this study is to propose a method which gives more suitable A and to evaluate the performance of it.

A method of simple calculation for the delete-one estimates in the likeli¬hood-based cross-validation (LCV) score is described. A score of similar form to the Akaike information criterion (AIC) is also derived. The proposed scores are compared with the ones of standard procedures by using data sets in liter¬atures. Simulations are performed to compare the patterns of selecting A and overall goodness-of-fit and to evaluate the effects of some factors. The LCV-scores by the simple calculation provide good approximation to the exact one if λ is not extremeiy smaii Furthermore the LCV scores by the simple size it possible to select X adaptively They have the effect, of reducing the bias of estimates and provide better performance in the sense of overall goodness-of fit. These scores are useful especially in the case of small sample size and in the case of binary logistic regression.     

A one-sided test for testino homogeneity of scale parameters against simple ordered alternative

In an earlier paper the authors (1997) extended the results of Hayter (1990) to the two parameter exponential probability model. This paper addressee the extention to the scale parameter case under location-scale probability model. Consider k (k≧3) treatments or competing firms such that an observation from with treatment or firm follows a distribution with cumulative distribution function (cdf) F_i(x)=F[(x-μ_i)/Q_i], where F(·) is any absolutely continuous cdf, i=1,…,k. We propose a test to test the null hypothesis H₀:θ₁=…=θ_k against the simple ordered alternative H₁:θ₁≦…≦θ_k, with at least one strict inequality, using the data X_i,j, i=1,…k; j=1,…,n₁. Two methods to compute the critical points of the proposed test have been demonstrated by talking k two parameter exponential distributions. The test procedure also allows us to construct simultaneous one sided confidence intervals (SOCIs) for the ordered pairwise ratios θ_j/θ_i, 1≦i<j≦k. Statistical simulation revealed that: 9i) actual sizes of the critical points are almost conservative and (ii) power of the proposed test relative to some existing tests is higher.     

The non-null distributions in anoya

Under the traditional assumptions, any entry in ANOVA interpreted to include all Linear model analyses] is equivalent in disiributien to a quadratic form Q=[μ₁+σ₁Z₁]²+…+ [μ_ν+σ_νZ_ν]²]wherein Z₁..Z_ν are independent standard normal variables. Test statisics in ANOVE are distributed as ratio R of two depenbent such quadretic forms. The non-null distribution of R is a mixture of null distributions; the mixing variable is an easy generalitatlon of the Poisson variable. Fast algorithms yield the power function in both fixed and random effects models in AVOVA to user-specified accuracy.     

A further note on a theorem on the difference of the generalized inverses of two nonnegative definite matrices

Andrews and Phillips (1986) gave a simplified proof for the result that established the nonnegative definiteness of the difference of the Moore-Penrose inverses of two nonoegative definite matrices, a result originally due to Milliken and Akdeniz (1977), The purpose of this paper is to offer a simple proof for a generalization of this result,     

Unbiased estimation of a nonlinear function a normal mean with application to measurement err oorf models

Let W be a normal random variable with mean μand known variance σ². Conditions on the function f(·) are given under which there exists an unbiased estimator, f(W), of f(μ) for all real μ. In particular it is shown that f(·) must be an entire function over the complex plane. Infinite series solutions for F(·) are obtained which are shown to be valid under growth conditions of the derivatives, f^k( ·), of f(·). Approximate solutions are given for the cases in which no exact solution exists. The theory is applied to nonlinear measurement-error models as a means of finding unbiased score functions when measurement error is normally distributed. Relative efficiencies comparing the proposed method to the use of conditional scores (Stefanski and Carroll, 1987) are given for the Poisson regression model with canonical link.