Statistical Dgiagnosis Of Single Index Modal Models

In the fields of astronomy,finance,economy,engineering technology and biomedical science,data distribution often shows the characteristics of highly spikes and heavy-tail,and the density distribution is asymmetric and skewed.In the case,single index modal models are the important ways to describe these features.Because the single index modal models are the improvements of single index model and modal regression.On the one hand,single index models can reduce the multidimensional covariate to a one dimension index,thus can overcome the weakness of the curse of dimensionality.On the other hand,the mode of a distribution provides an important summary of data,which is a very important feature of data.Especially when there exist outliers in the data or the error distribution is skewed,modal regression can provide more meaningful point prediction and larger coverage probability for sample than the mean regression.In this paper,for single index models,we devote to exploring statistical diagnosis and local influence analysis based on case-deletion model(CDM)and mode-shift outlier model(MSOM).After this work,we obtained some new results that have not been reported in domestic and foreign literature,which is very meaningful not only in the statistical theory and method,but also have made more extensive and great application in various fields.In addition,Bayesian analysis of the single index modal models are also studied in this paper,we use the spline to approximate to the unknown function and use the priori Markov Chain Monte Carlo simulation method(MCMC)to get sample from the conditional posterior distribution.Thus we can obtain the Bayesian estimation about the unknown parameters and unknown function of the model,and on this basis,we also study the Bayesian local influence analysis of such models.Finally,we illustrate the proposed models and methods with a simulation study and an analysis of Boston housing data set.