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Statistical Methods with Applications to Demography and Life Insurance
book

Statistical Methods with Applications to Demography and Life Insurance

by Estate V. Khmaladze
March 2013
Intermediate to advanced content levelIntermediate to advanced
242 pages
5h 47m
English
Chapman and Hall/CRC
Content preview from Statistical Methods with Applications to Demography and Life Insurance
Lecture 11
Statistical inference about F,
based on the Kaplan–Meier
estimator
Before we consider three specific statistical problems let us quickly
look back on what was done in Lectures 9 and 10. The key model
derived there was that if we have censored observations, and if Y
n
is
the process of those “at risk”, then the process M
n
defined as
M
n
(t) = N
n
(t)
Z
t
0
Y
n
(s)µ(s)ds, 0 t < τ,
is a martingale with respect to the filtration {F
n
t
,0 t < τ}, where
each σ-algebra is generated by the past of Y
n
and N
n
up to the moment
t:
F
n
t
= σ {Y
n
(s),N
n
(s),s t}. (11.1)
This was done in the context where N
n
(t) counted the number of life-
times, or failure times, up to the moment ...
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Publisher Resources

ISBN: 9781466505742