Abstract

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.