Abstract
In this chapter, the nonparametric maximum likelihood estimate (NPMLE) for random variables under double-truncation is presented. In contrast to parametric approaches, no specific distributional assumptions are made, and it is described how the estimator originally derived in Efron and Petrosian (J Am Stat Assoc 94(447):824–834, 1999) is defined and motivated. It turns out that the solution to the estimation problem can be regarded as a fixed-point. We reproduce key ideas from Shen (Ann Inst Stat Math 62:835–853, 2010) who offered more extensive explanations and important insights on the likelihood alternatives. In addition, theoretical properties of the procedure including consistency are stated. The method is applied to the Equipment-S dataset.
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Dörre, A., Emura, T. (2019). Nonparametric Inference for Double-Truncation. In: Analysis of Doubly Truncated Data. SpringerBriefs in Statistics(). Springer, Singapore. https://doi.org/10.1007/978-981-13-6241-5_4
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DOI: https://doi.org/10.1007/978-981-13-6241-5_4
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