Bootstrap Inference And Application For Skew-normal Unbalanced Panel Model With One-way Error Component

Panel model with one-way error component is a commonly used mixed effects model in many fields,such as economy,finance,medicine,ecology,geology,industry,engineering.Many studies on this model are usually carried out under the assumption of normal distribution and balanced design structure.However,in the process of data acquisition and statistical modeling,unbalanced data with asymmetric skew-normal distribution is common.Therefore,due to the limitations of distribution assumption and design structure,the existing statistical inferences of such models lack robustness in practice,or even are no longer applicable.In view of this,we study the statistical inference theory of unbalanced panel model with one-way error component under the assumption of skew-normal distribution.Firstly,for skew-normal unbalanced panel model with one-way error component,based on the matrix decomposition technique,Bootstrap approach,generalized approach,Monte Carlo simulation and other statistical approaches,we study the estimation and hypothesis testing of regression coefficients and variance component functions.The theoretical properties of the given testing approaches and confidence intervals such as transformation invariance are proved.Secondly,the test statistics and confidence intervals of fixed effect and variance component functions are constructed by taking skew-normal unbalanced one-way classification random effects model as a special case,and the statistical inference theory is extended to the heteroscedasticity case.Thirdly,Monte Carlo numerical simulation is used to verify the statistical excellent properties of the proposed approaches.Finally,the research results are applied to analyze influence factors of the urban-rural income distribution gap in Zhejiang Province,and targeted countermeasures and suggestions are put forward.The results show that for skew-normal unbalanced panel model with one-way error component,the exact testing approach performs well for the hypothesis testing problems of the regression coefficients and ratio of variance components.In most cases,the Bootstrap approach is superior to the generalized approach for the testing problems of variance components and their sums.For skew-normal unbalanced one-way classification random effects model,the Bootstrap approach can effectively control the sizes for the testing problems of the fixed effect,single variance component and sum of variance components.For the ratio of variance components,the exact testing approach provides satisfactory performance in terms of the power.Further,in the case of heteroscedasticity,the Bootstrap approach is better than the generalized approach for the testing problems of variance component functions in the given sample sizes and parameter configurations.Through the systematic measurement and analysis of the factors influencing the urban-rural income disparity,it is apparent that Zhejiang Province has made significant strides in urban-rural integration,but a spatial pattern of unbalanced regional development persists.Notably,urbanization,industrial structure upgrading and sustained economic growth have emerged as crucial drivers in narrowing the urban-rural income gap in Zhejiang Province.