Statistical Diagnosis Of Partially Linear Single-index Models Based On Modal Regression

The mode of a distribution provides an important characteristic of data,and the modal regression shows many advantages based on this feature.Especially in recent years,it has been widely used in many fields of data analysis,and has been became a powerful tool for parameter estimation.For example,Yao and Li(2013)firstly put forward a new modal model and estimate parameter in linear modal model;Hu and Jiang(2014)give the estimation for partially linear single-index model based on modal regression.But there are no articles to consider statistical diagnosis based on modal regression,this paper will do statistical diagnosis for linear model and partial linear model on the basis of theirs.we make a study on the statistics diagnostic on the basis of deleted model and local influence analysis and so on,now the main research is as follows:1.Based on what Yao and Li(2013)had done,We have considered statistical diag-nosis on the basis of data deleted model and local influence analysis for the linear modal regression to determine whether some points may be the outliers or strong influence points.2.Based on what Hu and Jiang(2014)had done,we have conducted statistical diagnosis on the basis of data deleted model,modal drift model and local influence analysis of the model for partially linear single-index models based on modal regression.3.Following what Hu and Jiang(2014)had studies,we have proposed Bayes local influence analysis for partially linear single-index models based on modal regression.