(A) study on the nonparametric density estimation with the small censored data

Abstract

This thesis is concerned with the nonparametric kernel-type density estimation under the constraint of decreasing assumption when the observation is right-censored. When the largest obseration is censored, nonparametric maximum likelihood estimator (MLE) does not exist. So Vardi introduced the M-restricted MLE. The proposed estimator in this thesis can be considered the application of kernel method to M-restricted MLE. In simulation study for small sample, we observe that the proposed estimator has more small integrated mean squared error than other estimator. This fact indicates the proposed estimator is more effective and usable than other estimator when the sample is small.