Robust Statistics Of Semi-parametric Models With Longitudinal Data And Its Application In Influencing Factors Analysis Of Rural Residents' Consumption

As an organic combination of cross-sectional data and time series,longitudinal data has been widely used in social science,economics,biomedicine and other fields.Vertical data structure can effectively describe the internal correlation structure of data and provide more data information.Therefore,vertical data analysis can better reflect the correlation between things and improve the estimation efficiency.However,there is a certain intra group correlation between the data of longitudinal data.In statistical inference,if the intra group correlation is ignored and the statistical inference theory dealing with cross-sectional data is directly used for research,it will inevitably lead to the lack of information and the obtained estimation is often no longer effective.Aiming at the longitudinal data,by establishing the longitudinal semi parametric model,combining the QR decomposition technology of matrix and the quadratic inference function method,this paper proposes an estimation process based on modal regression,proves that the estimation of parameter components is consistent,and gives its asymptotic distribution.It is also proved that the estimates of nonparametric components are consistent,and the optimal nonparametric convergence rate is achieved.As a developing country,China's economy has maintained stable growth and development since the reform and opening up,but residents' consumption,as one of the factors driving the economy,has always been low.The living conditions of rural residents have not been fully synchronized with social development,and the consumption of rural residents is significantly low.In this case,studying the factors affecting the consumption of rural residents in China is of great practical significance to improve the consumption level of rural residents and promote the healthy development of China's economy.Therefore,as an application,this paper uses the proposed modal regression method to analyze the influencing factors of rural residents' consumption in China,and selects a total of 10 indicators including farmers' living conditions,farmers' production conditions and the current situation of social environment.The results show that the factors affecting the consumption of rural residents in China are complex.Firstly,the per capita disposable income and total grain output of rural residents have the greatest impact on the per capita living consumption expenditure of rural residents.It greatly stimulates the consumption of rural residents and promotes the development of rural economy.Secondly,the total output value of agriculture,forestry,animal husbandry and fishery,the dependency ratio of children,the dependency ratio of the elderly and the urbanization rate will effectively promote the increase and improvement of rural residents' consumption;At the same time,the consumption price index of rural residents,the total power of agricultural machinery,the sown area of crops and the ratio of medical expenditure will weaken the consumption of rural residents to a certain extent.Finally,combined with the analysis of China's rural residents' consumption situation and the results of empirical research on the factors affecting consumption from the perspective of improving China's rural residents' consumption level and living environment,this paper puts forward corresponding policy suggestions to increase rural residents' consumption.