# Nonparametric Estimation from Incomplete Observations

**E. L. Kaplan****Paul Meier**

CiteWeb id: 20120000000

CiteWeb score: 46928

In lifetesting, medical follow-up, and other fields the observation of the time of occurrence of the event of interest (called a death) may be prevented for some of the items of the sample by the previous occurrence of some other event (called a loss). Losses may be either accidental or controlled, the latter resulting from a decision to terminate certain observations. In either case it is usually assumed in this paper that the lifetime (age at death) is independent of the potential loss time; in practice this assumption deserves careful scrutiny. Despite the resulting incompleteness of the data, it is desired to estimate the proportion P(t) of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of the function P(t). The observation for each item of a suitable initial event, marking the beginning of its lifetime, is presupposed. For random samples of size N the product-limit (PL) estimate can be defined as follows: L...

Links:- www.scharp.org/users/yqchen/class/KaplanMeier1958JASA.pdf
- www.alterlab.org/teaching/BIOEN3070/papers/Kaplan_1958.pdf
- www.jstor.org/stable/2281868?seq=2
- amstat.tandfonline.com/doi/pdf/10.1080/01621459.1958.10501452
- www.tandfonline.com/doi/abs/10.1080/01621459.1958.10501452
- link.springer.com/chapter/10.1007/978-1-4612-4380-9_25
- amstat.tandfonline.com/doi/abs/10.1080/01621459.1958.10501452
- dx.doi.org/10.1080/01621459.1958.10501452
- en.journals.sid.ir/ViewPaper.aspx?ID=88095
- www.jstor.org/pss/2281868

E. L. Kaplan, Paul Meier,

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