October 2014
Intermediate to advanced
584 pages
22h 2m
English
Content preview from Pricing in General Insurance
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459Rating Factor Selection and Generalised Linear Modelling
Let us now see what happens if, instead of having a single dependent variable, we have
k different variables so that the model in Equation 26.1 becomes
yfxx ax b
iiik irir i
r
k
=…+= ++
=
∑
(, )
,, ,1
1
εε
(26.4)
This can be written fully as
y
y
y
xx
xx
n
k
k
1
2
11 1
21 2
1
1
1
…
=
…
…
…………
,,
,,
xxx
b
a
a
nnk
k
,,1
1
1
2
…
…
+
ε
ε
……
ε
n
and in shorthand vectorial format as
Y = Xβ + ε (26.5)
where Y = {y
1
,…y
n
}
T
is the vector of observations, β = {b, a
1
,…a
k
}
T
is the vector of the
parameters,
X =
…
…
…………
…
1
1
1
11 1
21 2
1
xx
xx
xx
k
k
nn
k
,,
,,
,,
is the input vector (x
i,j
represents ...
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