Imputation Methods For Quantile Estimate With Missing Data

Compared with mean estimation and variance estimation,the quantile estimate does not need the parameter distribution hypothesis,so it is more suitable for the sample data showing non-normal distribution,such as household income and expenditure,biomedicine,financial risk measure and so on.However,in the process of sample acquisition,the existence of missing data is caused by various reasons,which will affect the estimated quality and increase the error of the estimation result,which may cause misjudgment of the research problem.Considering that there are many scholars have studied the overall mean estimate of missing data,this paper focuses on the estimation of the overall quantile estimate with missing data.In this paper,two methods are proposed to deal with this problem:one is the fractional hot deck imputation and the other is the nonparametric fractional imputation.These two imputation methods are derived from the fractional imputation method.The imputation values are derived from the observed data rather than the conditional distribution.Therefore,the parameter distribution hypothesis is not required in the estimation and the distribution of the original data can be maintained to the greatest extent.And thus the estimated results are more robust than the results of the imputation model assumptions.Through the simulation study,the process of these two methods to verify the process,and select nearest neighborhood imputation,multiple imputation and parameter fraction imputation for comparison,demonstrated in this paper,the two methods in the non-normal distribution,after the interpolation of the quantile estimated accuracy is higher,with a wider range of practical application value.In the empirical study,the fractional hot deck imputation and the nonparametric fractional imputation are applied to the household survey data,and the data missing items are interpolated and the quantile is estimated.