Abstract
Length-biased and censored data may appear when analyzing times of duration In this work, a new empirical curve \(\tilde F\) for approximating a distribution functionF under right-censoring and length-bias is introduced. The proposed estimate is (not equal to but) closely related to the product-limit Kaplan-Meier estimator. Strong consistency and distributional convergence is established for a general empirical parameter \(\tilde \gamma = g\left( {\int {\varphi _1 d\tilde F} ,...,\int {\varphi _\tau d\tilde F} } \right)\). As applications, one can obtain the corresponding large sample results for estimates of the distribution function, the cumulative harard function, and the mean residual time function. The new method is illustrated with real data concerning unempoloyment duration.
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Dedicated to the memory of Alejandro and José-Luis de Uña-Álvarez.
Work supported by the DGES grant PB98-0182-C02-02 and the Xunta de Galicia grant PGIDT00PXI20704PN.
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de Uña-Álvarez, J. Product-limit estimation for length-biased censored data. Test 11, 109–125 (2002). https://doi.org/10.1007/BF02595732
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DOI: https://doi.org/10.1007/BF02595732