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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
92 Estimation of the rate of mortality
and smaller, using more and more intricate methods to extract “local
information” in the neighborhood of x.
Let us present a general way of doing this. Starting with a function
K(z), such that
Z
K(z)dz = 1, (8.8)
transfer it into a kernel
1
K
x y
.
This kernel is now a function of two variables, x and y, and for any x,
as a function of y it is more and more “concentrated” around x as
becomes smaller.
Now consider the integral
e
f
n
(x) =
1
Z
K
x y
d
b
F
n
(y) =
1
n
n
i=1
K
x T
i
as an estimator of a density f (x) at point x. For example, if K(z) =
I
{−1z0}
, then
1
K
x y
=
1
I
{xyx+}
and
e
f
n
(x) =
b
f
n
(x),
and if K(z) = I
{−
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Publisher Resources

ISBN: 9781466505742