Local M-estimation Of Varying Coefficient Models And Its Special Type

Non-parametric regression model shows the performance of a powerful processingcapability in dealing with one-dimensional problems. Variable coefficient model methodplays an important part in dealing with high-dimensional data. It is simple, easy tounderstand and estimate and it also retains the stable characteristics of the non-parametricregression model. It contains both parameter information and non-parametric information,enhancing the adaptability of the model and overcoming the problem of informationoverload in non-parametric method.The paper mainly research local M-estimation of semi-varying coefficient model andthe varying coefficient models with missing data. Specific arrangements are as follows:Firstly, under the condition of independent and identical distribution, the paperdiscusses semi-varying coefficient model by local M-estimation, and proves theconsistency and asymptotic normality of the coefficient functions and unknownparameters. The use of local M-estimators inherits advantages of partial least squaresregression, and overcomes the shortcomings as lack of robustness. On the basis, a variablebandwidth is embedded and the plasticity of estimate is improved further. The localM-estimation requires the numerical iteration scheme and calculated amount is very large.In order to reduce the problem, a variable bandwidth and one step local M-estimation isintroduced, so that the computational burden is reduced. And it is proved that when theinitial estimate of a reasonable good, it has the same asymptotic performance as the localM-estimation.Secondly, in the paper, variable coefficient model is researched in the case of missingresponse variables. By variable bandwidth local M-estimation the parameter estimationmethod is given, and it is proved when the initial estimate is reasonably good, the sameasymptotic performance as a step local M-estimation.Finally, in dealing with missing data, two methods are used: firstly, the pairwisedeletion method, that is the pairwise deletion of the response variable with missing data,and estimating with the remaining data; secondly, estimation method, that is estimation of the simple method instead of response variables with missing data, forming a completedata set, and then estimating the coefficient parameters. In both methods, thecorresponding estimation function is derived, and their asymptotic mean square errorexpression is given then the advantages of both methods are compared.