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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
136 Statistical inference, based on Kaplan–Meier estimator
Under the first choice, the martingale M
m,n
becomes
M
m,n
G
(t) =
1
p
mn(m + n)
Z
t
0
[Y
2m
(s)dN
1n
(s) Y
1n
(s)dN
2m
(s)],
and its quadratic variation becomes
hM
m,n
G
i(t) =
Z
t
0
Y
1n
(s)
n
Y
2m
(s)
m
Y
1n
(s) +Y
2m
(s)
m + n
µ(s)ds.
We approximate this quadratic variation by
A
m,n
G
(t) =
Z
t
0
Y
1n
(s)
n
Y
2m
(s)
m
dN(s),
which is also computationally simpler cf. Breslow and Crowley
[1970], where A
m,n
G
() was considered.
To verify the conditions of the central limit theorem for M
m,n
G
is
easy. The resulting statement is
if the hypothesis (11.13) is true and m,n , then
M
m,n
G
d
W = w A
G
,
where
A
G
(t) =
Z
t
0
[1 G
1
(s)][1 G
2
(s)][2 G
1
(s) G
2
(s)][1
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Publisher Resources

ISBN: 9781466505742