This paper considers a widely used mixed effects model in repeated measures under het- eroscedasticity. Hypotheses of the equality of the fixed effects and the simultaneous confidence intervals for all pair-wise diffe...This paper considers a widely used mixed effects model in repeated measures under het- eroscedasticity. Hypotheses of the equality of the fixed effects and the simultaneous confidence intervals for all pair-wise differences are discussed. A generalized F-test has been proposed to test the equality of the fixed effects in the model, but simulation results for evaluating its performance have not been shown in the literature. Moreover, the generalized F-test cannot be used to deduce the simultaneous confidence intervals for all pair-wise differences of the fixed effects. The authors propose two new p-values to test the hypotheses of equality of the fixed effects and simultaneous confidence intervals of the differences of the effects based on the generalized pivotal quantities derived in this paper. The authors also compare the empirical performances of the proposed tests and the generalized F-test. The type I error rates and powers of these tests are evaluated using the Monte Carlo simulation. The simulation studies show that the generalized F-test does not perform well in terms of type I error rate under various sample size and parameter combinations. However, the type I error probabilities of the proposed tests are always close to the nominal value. It can also be seen that the simultaneous confidence intervals perform well.展开更多
A model that,scheduling a set,of stochastic jods on a single machine that is subject to breakdorwn and repair is dicussed.The model assumes that a significant set-up time,which is an arbitrary variable,is when the mac...A model that,scheduling a set,of stochastic jods on a single machine that is subject to breakdorwn and repair is dicussed.The model assumes that a significant set-up time,which is an arbitrary variable,is when the machine changes from processing one of jobs to another job.When job i is being processed, the prooessing time of job i,uptime and reparied time of the machine are all general random variables. For both preemptive resume model and preemptive repeat model,we find the optimal polices that minimize the following objective functions:(1)the weighted sum of the completion times;(2)the weighted number of late jobs having random dud dates with exponential distributions.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11126243 and 11071015Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality(PHR 201107123)School Scientific Found under Grant No. 101002207
文摘This paper considers a widely used mixed effects model in repeated measures under het- eroscedasticity. Hypotheses of the equality of the fixed effects and the simultaneous confidence intervals for all pair-wise differences are discussed. A generalized F-test has been proposed to test the equality of the fixed effects in the model, but simulation results for evaluating its performance have not been shown in the literature. Moreover, the generalized F-test cannot be used to deduce the simultaneous confidence intervals for all pair-wise differences of the fixed effects. The authors propose two new p-values to test the hypotheses of equality of the fixed effects and simultaneous confidence intervals of the differences of the effects based on the generalized pivotal quantities derived in this paper. The authors also compare the empirical performances of the proposed tests and the generalized F-test. The type I error rates and powers of these tests are evaluated using the Monte Carlo simulation. The simulation studies show that the generalized F-test does not perform well in terms of type I error rate under various sample size and parameter combinations. However, the type I error probabilities of the proposed tests are always close to the nominal value. It can also be seen that the simultaneous confidence intervals perform well.
文摘A model that,scheduling a set,of stochastic jods on a single machine that is subject to breakdorwn and repair is dicussed.The model assumes that a significant set-up time,which is an arbitrary variable,is when the machine changes from processing one of jobs to another job.When job i is being processed, the prooessing time of job i,uptime and reparied time of the machine are all general random variables. For both preemptive resume model and preemptive repeat model,we find the optimal polices that minimize the following objective functions:(1)the weighted sum of the completion times;(2)the weighted number of late jobs having random dud dates with exponential distributions.
