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Smooth nonparametric estimation of the distribution and density functions from record-breaking data. (English) Zbl 0825.62160
Summary: In some experiments, such as destructive stress testing and industrial quality control experiments, only values smaller than all previous ones are observed. Here, for such record-breaking data, kernel estimation of the cumulative distribution function and smooth density estimation is considered. For a single record-breaking sample, consistent estimation is not possible, and replication is required for global results. For $$m$$ independent record-breaking samples, the proposed distribution function and density estimators are shown to be strongly consistent and asymptotically normal as $$m\rightarrow\infty$$. Also, for small $$m$$, the mean squared errors and biases of the estimators and their smoothing parameters are investigated through computer simulations.

##### MSC:
 62-XX Statistics
##### Keywords:
record samples; kernel estimation; consistency
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##### References:
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