Group sequential x2 statistic for testing the difference of two mean vectors in clinical trials

In this study we discuss the group sequential procedures for comparing two treatments based on multivariate observations in clinical trials. Also we suppose that a response vector on each of two treatments has a multivariate normal distribution with unknown covariance matrix. Then we propose a group sequential x² statistic in order to carry out repeated significance test for hypothesis of no difference between two population mean vectors. In order to realize the group sequential test where average sample number is reduced, we propose another modified group sequential x² statistic by extension of Jennison and Turnbull ( 1991 ). After construction of repeated confidence boundaries for making the repeated significance test, we compare two group sequential procedures based on two statistics regarding the average sample number and the power of the test in the simulations.     

Surveillance of the interaction parameter of the ising model

Surveillance to detect changes of spatial patterns is of interest in many areas such as environmental control and regional analysis. Here the interaction parameter of the Ising model, is considered. A minimal sufficient statistic and its asymptotic distribution are used. It is demonstrated that the convergence to normal, distribution is rapid. The main result is that when the lattice is large, all approximations are better in several respects. It is shown that, for large lattice sizes, earlier results on surveillance of a normally distributed random variable can be used in cases of most interest. The expected delay of alarm at a fixed level of false alarm probability is examined for some examples.     

Covariate classification by post–stratification

The plug–in Anderson's covariate classification statistic is constructed on the basis of an initially unclassified training sample by means of posty–stratification. The asymptotic efficiency relative to the discriminant based on an initially classified training sample is evaluated for the case where a covariate is present. Effect of post–stratification is examined.     

Estimation of the multi-criteria worths of the alternatives in a hierarchical structure of comparisons

The aggregated worths of the alternatives, when compared with respect to several criteria, are estimated in a hierarchical comparisons model introduced by Saaty (1980). A multiplicative model is used for the paired comparisons data which are collected in a ratio scale in this set-up in any level of this hierarchy. An iterative scheme is found for the maximum likelihood estimation of the worth parameters in this multiplicative model. The iterative values are shown to be convergent monotonically to the estimates. We also obtain the asymptotic dispersion matrix of the maximum likelihood estimates of the relative worths of the alternatives according to a single criterion as well as those according to the over-all suitability when compared under several criteria. A numerical example is presented to illustrate the method developed in this paper. Simulation techniques are employed to find the average number of iterations required for the convergence of the above iterative scheme.     

A modification of watson's statistic for goodness-of-fit

A modification of Watson's statistic is suggested for dealing with stochastically ordered alternatives in the goodness-of-fit setting.     

A two-sample parametric group sequential procedure for monitoring clinical trials

A group sequential procedure is presented which allows for staggered entry of patients, random loss to followup, and utilizes the flexible boundary approach of Lan and DeMets. The proposed procedure assumes that response times are nearly exponentially distributed. An example as well as simulation studies comparing the performance of the proposed procedure with the group sequential logrank are also presented.     

Local Power Analyses of Goodness-of-fit Tests for Copulas

Abstract.  The asymptotic behaviour of several goodness-of-fit statistics for copula families is obtained under contiguous alternatives. Many comparisons between a Cramér–von Mises functional of the empirical copula process and new moment-based goodness-of-fit statistics are made by considering their associated asymptotic local power curves. It is shown that the choice of the estimator for the unknown parameter can have a significant influence on the power of the Cramér–von Mises test and that some of the moment-based statistics can provide simple and efficient goodness-of-fit methods.     

Cumulative correspondence analysis of ordered categorical data from industrial experiments

Most studies of quality improvement deal with ordered categorical data from industrial experiments. Accounting for the ordering of such data plays an important role in effectively determining the optimal factor level of combination. This paper utilizes the correspondence analysis to develop a procedure to improve the ordered categorical response in a multifactor state system based on Taguchi's statistic. Users may find the proposed procedure in this paper to be attractive because we suggest a simple and also popular statistical tool for graphically identifying the really important factors and determining the levels to improve process quality. A case study for optimizing the polysilicon deposition process in a very large-scale integrated circuit is provided to demonstrate the effectiveness of the proposed procedure.     

求凸二次函数极值的一种递推算法

本文通过讨论凸二次函数的几个结论,给出了求凸二次函数极值的一种递推算法．