The Study Of Sparse Strategies On Semi-Parametrical Models

With the rapid development of the era of big data,people are faced with redundant information and complex data structure,which makes the traditional statistical estimation model and theory no longer have good application performance.After nearly20 years of development,the sparse method plays an important role in the selection of important variables in the data and the improvement of the interpretability of the statistical model.However,due to the multi-constraints,non-singleness and high noise of complex data,the traditional sparse method based on linear regression is limited.Based on the classical sparse model,this paper studies the application of this technique in partial linear model,and further discusses the theoretical and practical performance of the sparse method in the high-dimensional conditional quantile half parameter model average.When applying the sparse method to the semi parametric model,this paper first considers the partial linear model.For the parameter structure of partial linear model,this paper uses different compression estimation strategies to study the influence of compression estimation on the estimation effect of partial linear model.By comparing the asymptotical distribution skewness and asymptotical risk of each strategy,the specific effects of different compression strategies are given theoretically.Finally,a new parameter estimation model of partial linear model based on difference method is established by using SCAD penalty function.Both numerical simulation and case study show that sparse method can improve the performance of traditional partial linear model.Before applying sparse method to quantile semi parametric model averaging,this paper studies the theory and calculation method of model averaging,and discusses the stationary model averaging method of generalized semi variable coefficient model in the case of discrete response variables.The new method develops the original model based on continuous response variables to discrete random variables.Firstly,the generalized semi variable coefficient model is considered as a candidate sub model.Then,the weight of each model is estimated by cross validation.In order to improve the accuracy and stability of model prediction,a new random segmentation model is designed.Finally,in order to weigh the performance of the new model in practical problems,this paper greatly enhances the robustness of the new model and significantly reduces the risk of the model's rough choice.It is found that the existing methods cannot solve the problem of data prediction with high noise.In this paper,we propose a high dimensional conditional quantile semi parametric model averaging problem with penalty terms.First,the marginal quantiles of each variable are calculated by a local linear regression method.By introducing a radial linear combination of marginal quantile function,an approximate estimate of conditional quantile of response variable is obtained.Then,using nonparametric kernel estimation method,this paper uses penalty function to estimate the weight vector of the model.Then,this paper focuses on the sparsity method to select important variables,so as to reduce the complexity and cost of model calculation.Using the selected important variables,the specific form of conditional quantiles of joint multivariate was estimated.In the computer data simulation analysis and actual case test,the new model has better robustness and better prediction effect.