I have a sample of observations where about $30\%$ of the observations are right-censored. I want to fit a kernel density estimator to this sample but I have not found a standard method to do so. Is there any widely accepted methodology for fitting a KDE in the presence of censored observations?

  • $\begingroup$ Hmm, it is similar, but not quite the same situation as in zero-inflated data. In spatial statistics with truncated data you can weight points closer to the boundary, but that logic is not easily translated to censored data off-hand. $\endgroup$ – Andy W Feb 9 '16 at 14:54
  • $\begingroup$ Can you describe what sort of problem or sequence this data describes? $\endgroup$ – DWin Mar 31 '18 at 6:14

Kernel density estimates the empirical distribution, it doesn't "know" and "care" about the underlying distribution. By "empirical" we mean here that it uses only the observed data and makes minimal distributional assumptions. Obviously, if it uses the observed data, it cannot say anything about the censored, unobserved data. If you say that the distribution is censored, it means that you should have some notion of the underlying distribution, so you should use it to define a parametric model to estimate the density.

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