The Robust Analysis Of Chinese Children BMI Index Via Quantile Regressive Single Index Model

Since the 18th National Congress of the CPC,the Party and the government have attached great importance to the quality of life and health of the people.In order to explain the synergistic relationship between the improvement of living standard and the physical health status of residents,this paper studies the synergistic effect between the body mass index(BMI)and the income level of people in different regions of Chinese society.In this paper,I selected the BMI index and family income data of Chinese rural children from the CHNS data from 1989 to 2011 as my empirical analysis.People's BMI change with the change of our body and is influenced by a variety of factors,so it is not only the difference between individuals that affect the change of BMI,but also the longitudinal time effect.In the modeling process of empirical analysis,we take into account the intergenerational effect of parents' BMI index on their children,and use the nonparametric regression method to carry out partial regression iterative calculation.In the process of statistical modeling,both the longitudinal effect of time and the intergenerational characteristics of children's families are considered,which makes the empirical analysis more comprehensive and objective.The establishment of parametric model requires many assumptions.Once some assumptions are inconsistent with the data reality background,it is inevitably lead to the reduction of the fitting efficiency of the system model,and even the failure of the statistical inference process.In order to build a more broad data analysis tool with robust estimation function,we use quantile regression and local linear estimation methods in this study to build a robust single-indicator model suitable for panel data.Firstly,the linear quantile regression method is used in the parameter part of the single index model.This method can overcome the influence of observed outliers on the model mean structure,give more weight to the observed values of key information,and reduce the influence of outliers on partial regression.Secondly,for the non-parametric part of the model,we use the local linear estimation based on quadratic regression to get the robust estimation of the non-parametric part of the model,which makes the overall statistical inference process more reasonable and effective.Finally,we propose a fast convergence algorithm for the robust estimation of single-index model,and give the Bootstrap empirical distribution window width selection method based on two-step robust residuals.Based on the above,the important work of this paper is as follows:(1)Propose a single index model with robust estimation function and suitable for panel data.(2)The partial regression method is used to construct a fast convergence algorithm for the single index model.(3)The bandwidth selection method of Bootstrap empirical distribution based on two-step regression robust residual was proposed.(4)Apply the model fitting method to the data analysis of the relationship between BMI index and family income of Chinese children,and demonstrate its superiority over the existing methods.