Research On Generalized Inference Of Interest Parameters Under Several Types Of Models

Generalized inference is a statistical inference method that use generalized test variables and generalized pivotal quantities to test and estimate interest parameters.It performs well in small and medium samples and when there are nuisance parameters in the model.In recent years,generalized inference has been continuously applied to various statistical problems.This paper mainly discusses the application of generalized inference methods in several kinds of common parameter models.These models include two-parameter exponential distribution models,linear mixed effects models,generalized inverse exponential distribution models based on censored data,etc.The paper constructs the generalized pivotal quantities for interest parameters to obtained its generalized confidence interval and the generalized p-value of the hypothesis testing problem,through Monte Carlo(MC)method for simulation calculation.The main results are as follows:(1)The generalized inference is applied to the interval estimation problem of the mean,quantiles and survival probability of the two-parameter exponential distribution.The generalized confidence limits of the mean and quantiles are discussed,compared with the exact confidence limit(calculation is difficult)and the approximate confidence limit by MC methods,and consequence turns out that the confidence limits got by the method we supply are closer to the exact confidence limits;and the difficulty in calculating the exact confidence limits is endured;At the same time,the coverage probabilities and average interval length for the generalized confidence interval of the mean,quantile and survival probability are also calculated.The results show that compared with the approximate confidence interval,the coverage probability of the generalized confidence interval is closer the nominal level,and the average interval length is shorter.(2)This paper studies the statistical inference of variance components in linear mixed effects models.By constructing the generalized pivotal quantity of all interest parameters in the linear mixed effect model involves two variance components,the generalized confidence interval and the generalized p values of the interest parameter are researched.Value test,through the Monte Carlo simulation method,the coverage rate of the confidence interval and its average length,the probability of making the Type-I error and the power of the test are applied.At the same time,the results obtained are compared with the results of other methods.The conclusion proves the excellent properties of the generalized inference method.(3)The generalized fiducial distribution(GFD)function of the generalized inverse exponential distribution(GIE)is discussed,and the fiducial point estimate and generalized confidence interval of the parameter A and,8 are calculated based on the distribution function.Using the AMHG(Adaptive Metropolis-Hastings within Gibbs)sampling method to obtain the iterative value of the parameter,and the problem of the parameter pivotal equation being an implicit equation is solved.The method is compared with the Bayesian method and the large sample method with the asymptotic normal distribution.The simulation results show that the generalized inference method better on the model.(4)The application of generalized inference under the generalized inverse exponential distribution is discussed,and the statistical inference research of the generalized inverse exponential distribution based on progressive type-? right censored data and upper record values is given.For this inference problem,the pivotal equation of the parameters is firstly constructed,and then we calculate the corresponding generalized confidence interval depend on its generalized pivotal quantity.Finally,the coverage rate of the confidence interval and the average length of the confidence interval are obtained by the MC method,then the method is compared with Bayesian method,large sample method based on asymptotic normal distribution.The simulation consequent indicate that the generlized inference method has higher accuracy and application values.