Paper Title
Modified Kernels Estimators of Risk Function Numerical Studies and Example

We consider risk function estimation under random right censoring by modified kernels estimators introduced by Muller et al. These kernels estimators with varying bandwidths and varying kernels well correct boundary effects near the endpoints of the support and reduces the increase of the variance over the support. In this study we illustrate by numerical simulations the behavior of both classical unmodified and modified kernels estimators of the risk function.Under various lifetime models and random right censoring we show the advantage of modified kernels estimators on the base of L1 and L2-errors. Then we treat a real example of survival data of Colon cancer data by Laurie, JA. et al. We identify an underlying risk function candidate and estimate local biases and local variances. The study point out that this boundary corrections perform well in practice and shows a good behavior of the estimators on boundaries. It also lead to smaller integrated mean squared errors compared to the unmodified estimators. Key words - Risk function, Modified Kernel density estimator, Boundary effect, Boundary kernels, Data-adaptive bandwidth, Survival analysis.