Composite Quantile Regression And Empirical Analysis Of Single Index Variable Coefficient Model

With the development of the times,a large amount of data has been generated,and the improvement of technology has provided more possibilities for data processing.With the coming of the big data era,the amount of data has become larger and larger,and the data structure has become very complex.The performance of traditional parametric models in dealing with complex data will become worse,and non-parametric estimation is bred in this demand.Since the 1940 s,the application of non-parametric estimation in large sample statistics has been gradually developing.The single index variable coefficient model using non-parametric model has also been applied to large data processing.Single index variable coefficient model can reduce dimension and retain the characteristics of linear model which is easy to explain.Compared with simple variable coefficient model,it is more flexible and applicable.At present,single index variable coefficient model has been used in practice,and it has been applied in biomedicine,econometrics and other fields.Using conditional quantiles of independent and dependent variables for regression modeling,this method is called quantile regression.Compound quantile regression is further extended on the basis of quantile regression,and the method has strong robustness.The study of complex data is a new problem for researchers in the era,and the study of complex models is inevitable.In this paper,the composite quantile statistical method and large sample properties of single index variable coefficient model are studied.The specific contents are as follows:Firstly,based on the single index variable coefficient model,the quantile regression method is used to estimate the unknown parameters and functions of the model.Furthermore,the model is processed by compound quantile regression,and the estimates of unknown parameters and functions are obtained.Secondly,considering some regular conditions,we prove the large sample nature of the estimator.Finally,by comparing simulation with existing model algorithms,it is concluded that the method used in this paper outperforms traditional methods in estimating data with outliers or complex error distributions.In empirical analysis,a new data set which has not been used in previous studies is used,and different from traditional statistical analysis,a popular and effective machine science is introduced.The learning algorithm GBDT,we compare the performance of two different model algorithms in complex data sets.The results show that the method used in this paper has certain advantages under certain circumstances.