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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
Testing a parametric hypothesis 131
θ is one-dimensional and its estimator
b
θ is chosen as the root of the
equation
Z
e
T
(n)
0
h(s,θ)dM
n
(s,θ) = 0,
which is the maximum likelihood equation, then for the process
ξ
n
(t) =
1
(
R
τ
0
h
2
(s,
ˆ
θ)A
n
(ds,
ˆ
θ))
1/2
Z
t
0
h(s,
b
θ)M
n
(ds,
b
θ)
the limit statement
ξ
n
d
V = v F,
with
F(t) =
Z
t
0
h
2
(s,θ)A(ds, θ)
Z
0
h
2
(s,θ)A(ds, θ) ,
is true.
Therefore, one can derive statistical inference about F in exactly
the same way as we have seen it in Lecture 5.
What happens if both parameters are unknown and have to be es-
timated? As in the general case, we start with linear regression of
dM
n
(t,
b
θ) on
Z
τ
t
h(s,θ)dM
n
(s,θ) =
1
θ
1
[M
n
(τ,θ) M
n
(t,θ)]
R
τ
t
(
1
θ
2
+ s)d
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Publisher Resources

ISBN: 9781466505742