9.8 Suppose 0, and 02 are each unbiased estimators of 0, with Vô,) = o? and VÔ2) = o2. A new unbiased estimator for 0 can be formed by Ôg = aô, + (1 – a)ô2 (0 < a s 1). If 0, and 02 are independent, how should a be chosen so as to minimize V(ô3)?
9.8 Suppose 0, and 02 are each unbiased estimators of 0, with Vô,) = o? and VÔ2) = o2. A new unbiased estimator for 0 can be formed by Ôg = aô, + (1 – a)ô2 (0 < a s 1). If 0, and 02 are independent, how should a be chosen so as to minimize V(ô3)?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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9.8) Suppose θ^1 (theta hat) and θ^2 (theta hat) are each unbiased estimator of θ....
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![### Section 9.8
Suppose \( \hat{\theta}_1 \) and \( \hat{\theta}_2 \) are each unbiased estimators of \( \theta \), with \( V(\hat{\theta}_1) = \sigma_1^2 \) and \( V(\hat{\theta}_2) = \sigma_2^2 \). A new unbiased estimator for \( \theta \) can be formed by
\[
\hat{\theta}_3 = a\hat{\theta}_1 + (1 - a)\hat{\theta}_2
\]
where \( 0 \leq a \leq 1 \).
If \( \hat{\theta}_1 \) and \( \hat{\theta}_2 \) are independent, how should \( a \) be chosen so as to minimize \( V(\hat{\theta}_3) \)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc263b93e-aaf5-48bf-8f55-91ec8edef641%2F9a08f020-3dd3-4809-9434-e18f05b6e257%2Fahucl6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Section 9.8
Suppose \( \hat{\theta}_1 \) and \( \hat{\theta}_2 \) are each unbiased estimators of \( \theta \), with \( V(\hat{\theta}_1) = \sigma_1^2 \) and \( V(\hat{\theta}_2) = \sigma_2^2 \). A new unbiased estimator for \( \theta \) can be formed by
\[
\hat{\theta}_3 = a\hat{\theta}_1 + (1 - a)\hat{\theta}_2
\]
where \( 0 \leq a \leq 1 \).
If \( \hat{\theta}_1 \) and \( \hat{\theta}_2 \) are independent, how should \( a \) be chosen so as to minimize \( V(\hat{\theta}_3) \)?
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