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Abstract:
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A standard assumption when doing inference for $F$, the distribution of the survival time in the current status model, is that the observation time comes from a Lebesgue density on an interval. Inference in this scenario has been studied extensively. However, in many applications, it is more realistic to think of the observation times as coming from a grid on a time interval, with the distinct ones assumed to grow with the sample size but at a slower rate. We investigate inference under such observation time schemes and show that for sufficiently sparse grids, the limit distribution of $F$ at a fixed point is normal, while for dense grids the limit transitions to the non-Gaussian Chernoff's distribution. There is a particular grid resolution ($n^{-1/3}$) at which this transition happens and the limit at this particular resolution is different from either of the previous limits.
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