zbMATH — the first resource for mathematics

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.

62-XX Statistics
Full Text: DOI
[1] DOI: 10.1007/BF02480340 · Zbl 0456.62026
[2] DOI: 10.1214/aoms/1177699450 · Zbl 0147.18805
[3] Chandler K.N., Journal of the Royal Statistical Society 14 pp 220– (1952)
[4] DOI: 10.1214/aos/1176344261 · Zbl 0378.62050
[5] DOI: 10.1007/BF02480982 · Zbl 0522.62027
[6] DOI: 10.1214/aoms/1177700394 · Zbl 0171.38801
[7] DOI: 10.2307/2978044 · Zbl 0395.62040
[8] Hoel P.G., Introduction to Stochastic Processe (1972)
[9] DOI: 10.1137/1110024 · Zbl 0134.36302
[10] DOI: 10.1214/aoms/1177704472 · Zbl 0116.11302
[11] DOI: 10.2307/1266340
[12] DOI: 10.1002/nav.3800330317 · Zbl 0605.62027
[13] DOI: 10.1002/1520-6750(198804)35:2<221::AID-NAV3220350207>3.0.CO;2-2 · Zbl 0656.62045
[14] DOI: 10.1002/1520-6750(199108)38:4<599::AID-NAV3220380411>3.0.CO;2-C · Zbl 0728.62095
[15] DOI: 10.2307/2288567 · Zbl 0593.62037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.