A Comparative Study on the Performance of Gamma Kernels for Nonparametric Imputation

The problems with using the symmetric kernels for nonparametric density and regression estimators for nonnegative data have been widely discussed. The use of asymmetric kernels for nonparametric regression, focusing on gamma kernels, have been recently proposed based on two different angles: one by Chaubey et al. (2010) and the other one by Shi and Song (2013). These estimators are based on the density estimators proposed by Chaubey et al. (2012) and Chen (2000). In the present thesis, we explore the performance of these estimators in the context of nonparametric imputation method under strongly missing at random assumption that has not been investigated yet in the literature. It is found that under certain assumption on the regression function, the estimator of Chaubey et al. (2010) may have a slight advantage over Shi and Song (2013) estimator whereas in other cases the comparison is not conclusive and further investigation may be needed