Bootstrap Inference On The Variance Component Functions In The Two-way Random Effects Model

The two-way random effects model is a special kind of linear mixed model,which is widely used in quality control,experimental design,biomedical research,econometric modeling,market analysis and many other practical fields.In view of the wide applications of variance component,research has been done about its parameter estimation problems.Some estimation methods has been established including analysis of variance,maximum likelihood,spectral decomposition,and minimum norm quadratic unbiased estimation.These above mentioned methods,however,are adequate for single variance component in general,but not for direct application for statistical inference on variance component function.In this paper,based on the Bootstrap approach and generalized approach,the test statistics and interval estimation problems of variance component functions in the two-way random effects model are established.Firstly,in the two way random effects model,the test statistics and confidence intervals of the ratio and the sum of the variance components are constructed for the balanced case.Secondly,the statistical inference problems of variance component functions of two way random effects model are extended to the unbalanced case.Further,the excellent statistical properties of the Bootstrap approach are verified by the Monte Carlo simulation.Finally,using the above theoretical research results,this paper analyses the digital economy efficiency of Central China and draws relevant conclusions and suggestions.The simulation results indicate that,based on the statistical inference of the ratio and sum of the variance components in the balanced and unbalanced two-way random effect model,the Bootstrap approach and generalized approach both can efficiently control Type I error probabilities,but the powers of the Bootstrap approach are apparently better than those of the generalized approach.In the unbalanced case,these two approaches are not influenced by the degree of imbalance,whether for the sum or ratio of variance components.Therefore,it can be concluded that the Bootstrap method performs better than the generalized method in most sample sizes and parameter settings.In actual case analyses,the excellent statistical properties of the Bootstrap approach are verified.