Model Mean Confidence Intervals For Several Scenario

Model averaging is becoming more and more popular as a statistical inference method that can solve model uncertainty.It is established for some shortcomings of model selection in statistical inference.In many cases,model averaging can replace model selection method,and with the improvement of computer technology,model averaging will be used more and more as a more complex data mining method.In many applications,it is increasingly common to consider model uncertainties when providing parameter estimates and confidence intervals.With the further study of model averaging,the application of model averaging extends from point estimation to interval estimation.At present,the commonly used methods for constructing model averaged confidence intervals include Wald interval and MATA-Wald interval.The Wald interval is centered on the average estimate of the model,and its range is determined by the estimation of the standard deviation of the estimated value.The MATA confidence limit satisfies that the weighted average of the error rate of each candidate model is equal to the required overall error rate.These intervals are constructed under the condition of asymptotic normal distribution of parameter estimation.In dissertation,we use the Bootstrap distribution of parameter estimation to approximate the real distribution of parameter estimation,and then the averaged confidence interval of Bootstrap model is proposed.The performance of these three methods under normal data and skewed data is simulated and compared respectively.Although randomness of weight is mentioned in the method theory of model averaged confidence interval,in the algorithm of model averaged confidence interval proposed by FMA method,model weight vector is obtained according to some information criteria.Based on the asymptotic distribution of weight and in the framework of linear nested model,this paper proposes the asymptotic confidence intervals of MMA,JMA and modified JMA prediction mean estimation,and compares them with many methods.