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Even if the variance is low, the cluster of arrows may still be far off-target, and even if the variance is high, the diffuse collection of arrows may still be unbiased. Asymptotic efficiency is the sufficient condition that makes OLS estimators the best estimators. Hence, asymptotic properties of OLS model are discussed, which studies how OLS estimators behave as sample size increases. As a result, they will be more likely to give better and accurate results than other estimators having higher variance. push({});
Basic Statistics and Data Analysis 2022.
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That the error for one estimate is large, does not mean the estimator is biased. 0001pt;
mso-pagination:widow-orphan;
font-size:11. ”A2. One can show that
{\displaystyle {\widehat {\theta }}}
is an unbiased estimator for
{\displaystyle \theta }
:
E
[
]
=
E
[
4
/
n
N
1
2
]
{\displaystyle E[{\widehat {\theta }}]=E[4/n\cdot N_{1}-2]}
=
4
/
n
E
[
N
go 1
]
2
{\displaystyle =4/n\cdot E[N_{1}]-2}
=
4
/
n
n
p
1
2
{\displaystyle =4/n\cdot np_{1}-2}
=
4
p
1
2
{\displaystyle =4\cdot p_{1}-2}
=
4
1
/
4
(
+
2
)
2
{\displaystyle =4\cdot 1/4\cdot (\theta +2)-2}
=
+
2
2
{\displaystyle =\theta +2-2}
=
{\displaystyle =\theta }
.
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.