A Bayesian Approach for Bandwidth Selection in Kernel Density Estimation with Censored Data

Estimating an unknown probability density function is a common problem arising frequently in many scientific disciplines. Among many density estimation methods, the kernel density estimators are widely used. However, the classical kernel density estimators suffer from an intrinsic problem as they assign positive values outside the support of the target density. This problem is commonly known as the ’Spill over’ effect. A modification to the regular kernel estimator is proposed to circumvent this problem. The proposed method uses a lognormal kernel and can be used even in the presence of censoring to estimate any density with a positive support without any spill over at the origin. Strong consistency of this estimator is established under suitable conditions. A Bayesian approach using as inverted gamma prior density is used in the computation of local bandwidths. These bandwidths yield better density estimates. It was shown that these bandwidths converge to zero for suitable choices of prior parameters and as a result the density estimator achieved its asymptotic unbiasedness. A simulation study was carried out to compare the performance of the proposed method with two competing estimators. The proposed estimator was shown to be superior to both competitors under pointwise and global error criteria.