Actuarial Notes

CAS Exam MAS-I Spring 2019, Question 17

Study guide: Exam MAS-I

You are given the following information:

$\tau$ is a parameter of a distribution
The true value of $\tau$ is 2
$\hat{\alpha}$ and $\hat{\beta}$ are two uncorrelated estimators for $\tau$
$E(\hat{\alpha}) = 2.0$
$\operatorname{Var}(\hat{\alpha}) = 5.0$
$E(\hat{\beta}) = 3.0$
$\operatorname{Var}(\hat{\beta}) = 1.0$

Consider the class of estimators of $\tau$ which are of the form: $w\hat{\alpha} + (1 - w)\hat{\beta}$ .

Calculate the value of $w$ that results in an estimator with the smallest mean squared error.

A) Less than 0.2
B) At least 0.2, but less than 0.4
C) At least 0.4, but less than 0.6
D) At least 0.6, but less than 0.8
E) At least 0.8

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