Testing Serial Correlation In Linear Model With High Dimensional Data

Generally,the data whose dimension is larger than the sanple size is usually called high-dimensional data.In the situation of high-dimensional data,conventional statistical methods have failed.In order to process high-dimensional data,the usual method is dimensionality reduction,among which the most classic method is Lasso.In this paper,the dimension of explanatory variables is processed by L1 penalty function to reduce the dimension and accurately screen the information.Meanwhile,the model parameters are estimated.Linear model is the most basic and classic model in statistical models.It has a very wide range of applications.What’s more,the independent and identical disfribution of residuals is usually required in various studies.If the correlation test of residuals is not tested before the application of model,there will be many risks such as model misusing or invalid parameter estimation.For the test of serial correlation,a large number of scholars have made a certain degree of research,but it is rarely involved in the high-dimensional data.So this paper will discuss the serial correlation test in the high-dimensional data,using the eirpirical likelihood test and VT,P test at the same time.Also,this paper considers the performance of classic Lasso and Capped Lasso under the same test.For the serial correlation test of linear models with high-dimensional data,this paper considers the respective performance of the two methods in the scope of high-dimensional data.Firstly,the penalty function is used to reduce the dimensionality of the data,which makes it possible to solve the normal equations and to estimate the parameters.Secondly,under the null hypothesis,the test statistics are constructed by using the empirical likelihood and VT,P.We also prove the asyirptotic disfribution of the test statistics.We made some simulations to verify relevant theories in different sample sizes and data dimensions.The simulation in this article has got good results.Finally,we present two sets of actual data analyses for serial correlation test of linear models with high dimensional data.