Testing with replacement and the product limit estimator : (preprint)
Richard Gill · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1978
Let x 1 ,x 2 ,~ .. be a sequence of i.i.d.strictly positive r.v.'s with d.f.F. Define N(t) = #{j: x 1 + ••• + X. ~ t}.In "testing with replacement" ~ J n independent copies of N are observed each over the time interval [O,T]and we are interested in nonparametric estimation of F based on these ob-.servations.We prove consistency of the product limit estimator as n ➔ 00 for arbitrary F, and weak convergence for two cases: integer valued X.; and