Multilinear Model Based On Robust Estimation Methodsand Variable Selection

Linear models play a central role in modern statistical methods.These models can approximate the measurement of data structures within the entire definition or at least in a piecewise manner.Under the assumption that the form of population distribution is known,the parameter estimation of population distribution through samples is one of the most critical parts in the establishment of the linear model,which directly affects the correctness of the statistical model.In order to improve the accuracy of parameter estimation,scholars have conducted a lot of research,and many feasible parameter estimation methods have been adopted.This paper puts forward two new kinds of robust parameter estimation methods,which can solve the problem of complex collinearity and outliers in the data.It also proposes a new approach to the selection of robust variables,which can select variables within unknown data distribution of various types.First,consider the case where all explanatory variables are important.Combining with the previous estimation,we put forward two new estimation forms: 1.Robust two-parameter estimation(RTPE);2.Robust Restrict Liu estimation(RRLE).When multiple collinearity and outliers coexist in data,these two forms of estimates have very good estimate effect,compared with pure M robust estimation method as well as the simple Liu estimates,ridge estimate,constraint Liu estimates,double parameters estimation and Liu constrained estimation,etc.They are also better than the previously proposed robust Liu estimates and solid double parameter estimation,etc.In this paper,the advantages of the new estimation form and the non-robust form,the robust Liu estimation,the robust ridge estimation and the constrained Liu estimation are compared respectively under the mean square error and the mean square error matrix criterion.Numerical simulation results show that the new estimator is superior to other estimators under different parameter conditions,and the superiority of the new estimator is also proved in the following data examples.It shows that the new estimation proposed in this paper is feasible for practical application.In addition,when outliers or the error being double-tailed distributions coexist in explanatory variables aside from redundant variables exist therein,we use robust variable selection method for parameter estimation.Based on traditional variable selection,this paper introduces the ways of thinking and the patterns of parameter selection of two robust variable selection methods,namely,the weighted LAD-LASSO method and the adaptive robust LASSO method.On the basis of these methods,it then presents MIXW-R,a new method of robust variable selection,and introduces its method of parameter selection and its realization of relevant algorithms.This paper compares the new selection method of robust variables and the above-mentioned selection method of robust and non-robust variables when the error term is normal data and within the linear model in which there are outliers in heavy-tailed distribution and in variables.It also demonstrates the advantages of the new estimation in different data status by data simulation.