Abstract
Let (X i,Y i),i=1, 2,..., be i.i.d. vector valued random variables with unknown common marginal distribution functionsF(x) andG(x). One model of incomplete observations studied in the literature is the truncated model, where bothX i andY i are observed ifX i ≥Y i, and nothing can be observed otherwise. From this kind of observations, if any, we describe the modified nonparametric maximum likelihood estimators ofF(x). The law of the iterated logarithm for the uniform covergence is proved.
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This work is supported by the National Natural Science Foundation of China.
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He, S. Estimating a distribution function with truncated data. Acta Mathematicae Applicatae Sinica 10, 12–33 (1994). https://doi.org/10.1007/BF02006256
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DOI: https://doi.org/10.1007/BF02006256