Isotontic regression for interval censored survival data using an e-m algorithm

This paper develops a nonparametric model of the relationship between survival S and a dichotomous random variable X under the order constraint that P(X=1|S=s) is increasing (or decreasing) with s. The estimation procedure, called isotonic regression, has been studied in some depth for the case of uncensored data, but we give a methodology which is appropriate in the more general context of right, left, and interval censored data. An E-M Algorithm (Dempster et. al., 1977) is used for maximum likelihood estimation.     

On the design of comparative lifetime studies

In designing a study to compare two lifetime distributions, decisions are required about the study size, the proportion of observations in each group and the length of follow-up period. These aspects of study design are examined using a Bayesian approach in which the expected consequences of a particular choice of design are evaluated by the expected gain in infornlation.     

Handling cause of death in equivocal cases using the em algorithm

The statistical analysis of animal bioassays fore carcinogenicity often involves utilizing the cause of death of each animal. There is considerable disagreement among veterinary pathologists as to the reliability of cause of death information. Recent recommendations for assigning cause of death in animal studies have allowed for uncertainty on the part of the pathologist. This has given rise to data that contain acknowledged equivocal cases with respect to cause of death. The present paper proposes a method for incorporating these equiYocal cases into an existing estimation procedure that requires distinguishing between tumors that caused death and those that did not.     

An extension of the median test to analysis of variance

In a k-way analysis of variance model, the major concern is testing for main effects and for the presence of interaction between the factors. When the assumptions of normality and equal variances are satisfied, the appropriate test to use is the usual F-test for ANOVA. However, when the normality assumption is not satisfied then a robust or nonparametric test is needed to conduct the analysis. In this paper a nonparametric method based on cell counts is proposed. Each cell is divided into L subcells based on predetermined outpoints and the resulting frequencies are laid out in a contingency table. Then the Pearson x² and tne likelihood ratio tests are performed. A comparison with the classical ANOVA F-test indicates that the proposed method is preferable when the data comes from a thick-tailed highly skewed distribution.     

Mean intergrated squared error properties and optimal kernels when estimating a diatribution function

Let X₁,X₂,… X_n be a sample of independent identically distributed (i.i.d)random variables having an unknown absolutely continuous distribution function f with density f the twofold aim of his paper consists in, firstly deriving asymptotic expressions of the mean intergrated squared error (MISE) of a kernel estimator of F when f is either assumed to be continuous everywhere or problem of finding optimal kernels in these two cases is studied in detail.     

Improved bounds for moments of some rank statistics

Improved lower hounds are obtained for two parameters μ(F) and λ(F) which occur in the moments of linear rank statistics studied by Doksum, Hollander, Lehmann and Hsu. IT is shown that if F is a continuous distribution, then μ(F) > 3/10 and λ(F) >= 89/315 - 0.28254. These results decrease the range of possible values of μ(F) and λ(F) by more than 84% and 34%, respectively, over those previously reported.     

A plug-in technique in nonparametric regression with dependence

The problem addressed is that of smoothing parameter selection in kernel nonparametric regression in the fixed design regression model with dependent noise. An asymptotic expression of the optimum bandwidth parameter has been obtained in recent studies, where this takes the form h = C ₀ n ^?1/5. This paper proposes to use a plug-in methodology, in order to obtain an optimum estimation of the bandwidth parameter, through preliminary estimation of the unknown value of C ₀.     

Sensitivity analysis for two control groups

In many experiments where data have been collected at two points in time (pre-treatment and post-treatment), investigators wish to determine if there is a difference between two treatment groups. In recent years it has been proposed that an appropriate statistical analysis to determine if treatment differences exist is to use the post-treatment values as the primary comparison variables and the pre-treatment values as covariates. When there are several outcome variables, we propose new tests based on residuals as alternatives to existing methods and investigate how the powers of the new and existing tests are affected by various choices of covariates. The limiting distribution of the test statistic of the new test based on residuals is given. Monte Carlo simulations are employed in the power comparisons.     

Optimal control designs using predicting densities for the multivariate linear model

We provide an application of a variety of predicting densities to quality control involving multivariate normal linear models. We produce optimal control designs for single muleivaiiate future observations using predicting densities employing estimative, profile likelihood, Hinkley-Lauritzen, Butler, Bayesian, and Parametric Bootstrap methodologies. The decision-theoretic optimality criterion is an intuitively appealing quadratic consumer-producer risk function. The optimal control design arising from an optimal Kullback-Leibler frequentist prediction density is shown to coincide with that arising from an optimal Kullback-Leibler Bayesian predictive density. An example involving EVOP is provided to illustrate the methodology and to raise questions concerning the relative merics of the variety of predictive approaches in the quality control context.     

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.