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Variance comparison for Poisson exposure estimators
...
Area of mathematics
Probability and statistics
Statistical modelling
Generalized linear model
Poisson exposure model
Estimators for a Poisson exposure model
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Words: 29
The two variances are
var
(
θ
L
S
)
=
S
2
2
θ
S
3
,
var
(
θ
M
L
E
)
=
S
1
θ
.
(171)
Since
S
2
2
≤
S
1
S
3
by Cauchy-Schwarz, maximum likelihood has no larger variance, with equality when all positive exposures are equal.
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(8)
Estimators for a Poisson exposure model
Poisson exposure model
Generalized linear model
Statistical modelling
Probability and statistics
Area of mathematics
Mathematics
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