| Single index model is an important kind of semi-parametric model,it can avoid the "curse of dimensionality",presents its high flexibility in data modeling,it is exten-sively employed in realistic problems.Censored data is one common kind of data type in clinical medicine,economics and finance.We can employ proportional hazard re-gression model to handle censored data,proportional hazard regression model has the attribute that when explanatory variable increase by one unit,the risk will increase by a constant.This has limited the effectiveness of statistic analysis.So many statisticians propose proportional odds model,then unify two models by a simple transformation regression model,which largely improve the flexibility of modeling of censored data.Noting that one assumption of simple transformation is that the covariant impacts the transformation of life time linearly.So statisticians propose many semi-parametric and non-parametric models,for instance,variable coefficient transformation model and partially linear additive transformation model.Due to the complexity of estimation,few discussed single index transformation model.This paper focuses on single index trans-formation model,study the MLE by B spline approaching technique.Under some condi-tions,we give out some large sample properties.Through some data analysis,we proved the effectiveness of model and methods. |
