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Current status data with competing risks: Limiting distribution of the MLE. (English) Zbl 1216.62047

Summary: We study nonparametric estimation for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler “naive estimator.” In our paper, ibid., 1031-1063 (2008; Zbl 1360.62123) we proved that both types of estimators converge globally and locally at rate \(n^{1/3}\). We use these results to derive the local limiting distributions of the estimators. The limiting distribution of the naive estimator is given by the slopes of the convex minorants of correlated Brownian motion processes with parabolic drifts. The limiting distribution of the MLE involves a new self-induced limiting process. Finally, we present a simulation study showing that the MLE is superior to the naive estimator in terms of mean squared error, both for small sample sizes and asymptotically.

MSC:

62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
62N02 Estimation in survival analysis and censored data
62M99 Inference from stochastic processes
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)

Citations:

Zbl 1360.62123
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References:

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