Bandwidth Selection for Estimating the Mean Residual Life Function

Mean Residual Life (MRL) function has been of considerable interest in a wide range of fields. MRL has been applied to reliability theory, technical systems and survivorship studies in biomedicine, among many others. Non-parametric approach has been used to estimate MRL function and it is an appealing technique to use in this regard since it does not impose many restrictions on the underlying probability distribution. Local Linear (LL) estimator is a non-parametric kernel based technique recently developed which is based on local linear fitting techniques. LL estimator is known to reduce bias and boundary effects that exist in kernel estimators. In this pap em; we discuss the performance of this estimator for MRL using different kernels and bandwidths. The investigation reveals that the performance of this estimator for distributions (or models) with a Decreasing Mean Residual Life (DMRL) function is excellent. In addition, the Mean Squared Error (MSE) of LL estimator is considerably low when compared to that of empirical version of MRL function. We also demonstrate that performance varies significantly with different bandwidth selection methods.