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http://hdl.handle.net/2451/14774
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| Title: | PARAMETRIC ESTIMATION OF HAZARD FUNCTIONS WITH STOCHASTIC COVARIATE PROCESSES |
| Authors: | Berman, Simeon M.
Frydman, Halina |
| Issue Date: | 1997 |
| Publisher: | Stern School of Business, New York University |
| Series/Report no.: | SOR-97-11 |
| Abstract: | Let X(t), t âÂÂ¥ 0, be a real or vector
valued stochastic process and T a random killing-time of the process
which generally depends on the sample function. In the context of
survival analysis, T represents the time to a prescribed event (e.g.
system failure, time of disease symptom, etc.) and X(t) is a stochastic
covariate process, observed up to time T. The conditional distribution
of T, given X(t), t âÂÂ¥ 0, is assumed to
be of a known functional form with an unknown vector parameter
ø; however, the distributions of
X(â¢) are not specified. For an
arbitrary fixed ñ > 0 the observable data from
a single realization of T and X(â¢) is
min(T, ñ), X(t), 0
⤠t
⤠min(T, ñ).
For n âÂÂ¥ 1 the maximum likelihood
estimator of ø is based on n independent copies of
the observable data. It is shown that solutions of the likelihood
equation are consistent and asymptotically normal and efficient under
specified regularity conditions on the hazard function associated with
the conditional distribution of T. The Fisher information matrix is
represented in terms of the hazard function. The form of the hazard
function is very general, and is not restricted to the commonly
considered cases where it depends on
X(â¢) only through the present point
X(t). Furthermore, the process X(â¢) is
a general, not necessarily Markovian process. |
| URI: | http://hdl.handle.net/2451/14774 |
| Appears in Collections: | IOMS: Statistics Working Papers
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