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Comparisons Between Local Linear Estimator and Kernel Smooth Estimator for a Smooth Distribution Based on MSE Under Right Censoring

We propose a local linear estimator for a smooth distribution function based on censored data. This new estimator applies local linear techniques to observations from a regression model where the value of the product limit estimator equals the value of the true distribution plus an error term. We show that the advantage of using the local linear estimator over the smooth kernel estimator is that, for most commonly used kernel functions, local linear estimator has a smaller mean squared error than the kernel smooth estimator studied by Ghorai and Susarla (1990).