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Constructive identification of the mixed proportional hazards model
Author(s) -
Kortram R. A.,
Rooij A. C. M.,
Lenstra A. J.,
Ridder G.
Publication year - 1995
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1995.tb01469.x
Subject(s) - constructive , constructive proof , mathematics , estimator , cumulative distribution function , distribution (mathematics) , identification (biology) , function (biology) , hazard , base (topology) , statistics , calculus (dental) , discrete mathematics , pure mathematics , computer science , mathematical analysis , probability density function , medicine , botany , chemistry , organic chemistry , process (computing) , dentistry , evolutionary biology , biology , operating system
We give a new proof of the identifiably of the MPH model. This proof is constructive: it is a recipe for constructing the triple—regression function, base‐line hazard, and distribution of the individual effect—from the observed cumulative distribution functions. We then prove that the triples do not depend continuously on the observed cumulative distribution functions. Uniformly consistent estimators do not exist. Finally we show that the MPH model is even identifiable from two‐sided censored observations. This proof is constructive, too.