Exponential Tilting Likelihood Inference Of Gini Coefficient And Its Application

The Gini coefficient is an indicator to measure the equality of income distribution,the size of the Gini coefficient can accurately judge the gap between the rich and the poor.so it is particularly important to accurately estimate the Gini coefficient.The calculation of the Gini coefficient relies on income data,in real life,because income involves personal privacy,which makes income data often missing.Therefore,it is more practical to consider the estimation of Gini coefficient from the perspective of missing data.This thesis considers the statistical inference of the Gini coefficient in the case of complete data and missing data respectively,based on the standardized Gini mean difference calculation formula,In the complete data set,use exponential tilting likelihood to solve the unbiased estimation equation to obtain point estimate and asymptotic normal interval of the Gini coefficient,use Bootstrap method to construct percentile Bootstrap interval,t percentile Bootstrap interval and bias-corrected percentile Bootstrap interval of the Gini coefficient.In the missing data set,the missing mechanism is assumed to be missing at random,the missing model is Logistic regression model,use the covariate balancing propensity score to estimate the missing probability function,the unbiased estimation equation of Gini coefficient based on inverse probability weighting,use exponential tilting likelihood to solve the estimation equation to obtain the point estimate of the Gini coefficient.Furthermore,use Bootstrap method to obtain the bias-corrected percentile Bootstrap interval of the Gini coefficient.At the same time,this thesis has carried out a lot of simulation calculations,the simulation results show that the exponential tilting likelihood point estimation of the Gini coefficient satisfies the asymptotic unbiasedness and efficiency,and the larger the missing rate,the larger the bias of the point estimate and the lower the efficiency.At the 95% confidence level,the coverage probability of the asymptotic normal interval,percentile Bootstrap interval,t percentile Bootstrap interval and bias-corrected percentile Bootstrap interval of the Gini coefficient is close to 95%,which satisfies the efficiency and balance,and the greater the missing rate,the lower the efficiency of interval estimation.Finally,the empirical part of this thesis applies the exponential tilting likelihood inference of the Gini coefficient to the household economic data of the 2018 China Family Panel Studies.