Bootstrap Inference Of Location Parameters In Several Skew-normal Populations

In recent years,the real data of economics,physics and epidemiology often show obvious skewed and symmetric characteristics.In the existing research on comparing the location parameters in several populations,it's generally on the assumption of normal distribution.If we continue to use the traditional normal distribution assumption for statistical inference,it's easy to have statistical error with true values.In view of this,with the unknown scale parameters and skewness parameters,this paper considers the problem of homogeneous test of location parameters,and construct the confidence interval of common location parameter based on Bootstrap approaches in several skew-normal populations.In the research of homogeneous test of location parameters in several skew-normal populations.Firstly,the conditional test statistic is constructed and its approximate distribution is proved.Secondly,we estimate the unknown parameters based on the methods of moment and maximum likelihood estimation.Then we construct the Bootstrap test statistics and generalize the results of Xu(2016)^[1]from normal population to skew-normal population.Further,the Monte Carlo simulation results indicate that in terms of controlling the Type I error probability,the Bootstrap test statistics based on the moment estimator performs better than that on the maximum likelihood estimator.In the research of interval estimation and hypothesis testing problems for the common location parameter in several skew-normal populations.Firstly,we estimate the unknown parameters by the methods of moment and maximum likelihood estimation.Secondly,the Bootstrap confidence intervals and Bootstrap test statistics are constructed,which generalize the results given by Xu(2016)^[2]under several normal populations.Thirdly,the Monte Carlo simulation results indicate that the Bootstrap confidence interval based on the method of moment performs better than other three confidence intervals.At last,the above approaches are applied to the real data examples of regional gross product of China,turbine bearing performance and bioavailability in order to verify the reasonableness and effectiveness of the proposed approaches.