Variable Selection Of Partial Linear Single Index Model Based On Lasso Method

With the rapid development of science and technology, in recent years, the commercial finance, information technology, scientific research and other fields will produce a large number of high dimensional data, and the relevance between the data has become more and more complex, then how to deal with the high dimensional data and draw valid conclusions from the data are what we need to solve. As an important semi parametric model, the partial linear single index model has many advantages in dealing with high dimensional data, and the result of the prediction can be more close to the true model. In this paper, we select the appropriate part of the linear single index model, and use three different methods to study the variable selection problem of this model, the specific content is as follows:Firstly, using the adaptive group lasso method to estimate the parameters of the partially linear single index model, and using the oracle theorem to study the consistency and asymptotic normality of the partially linear single index model of the adaptive group lasso method and to prove the method has the oracle property.Secondly, using the method of adaptive elastic net to estimate the parameter of partially linear single index model and using the oracle theorem to study the consistency and the asymptotic of this method and to prove the method has the oracle properties and the group effect properties of the method.Then using the penalized relative partial derivative method to estimate the parameter of partially linear single index model and giving some related derivation processes of the penalized relative partial derivative method of partially linear single index model, and compressing the coefficients of the linear single index model, also compressing the relative values of the coefficients and the directional derivatives.Finally, according to the Beijing affects the quality of the air pollution index establish the appropriate partially linear single index model, using the three methods to analysis this model, comparing the advantages and disadvantages of the three methods and giving a better variable selection method of the partial linear single index model.