# Methods for estimating the survival function

I want to estimate the survival function $S(t_0)=1-F(t_0)$, at a specific point $t_0$ where $F$ is a continuous cumulative distribution function, based on an uncensored sample $x_1,..,x_n$ and a nonparametric estimator. So far, I am considering two estimators $\hat S(t_0)=1-\hat F(t_0)$, where $\hat F$ is

(1) Kernel density estimator

(2) The empirical CDF.

What other methods could I consider using?

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Kaplan-Meier is the standard non-parametric survival estimator, which I'm guessing is what you meant by empirical CDF. You can get confidence intervals by various means with it so unless you want to go down a parametric route or start looking for more interesting things about the data I would say you're done!

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Thanks for the connection with the Kaplan-Meier estimator. –  IwillSurvive Aug 18 '12 at 11:56
Since the OP indicates there is no censoring, the K-M estimator corresponds exactly to subtracting the empirical cdf from 1. –  cardinal Aug 18 '12 at 13:54
I agree with you cardinal. –  IwillSurvive Aug 18 '12 at 14:07
Thanks, I am going to consider that I am not missing an alternative obvious estimator. –  IwillSurvive Aug 18 '12 at 18:47