If T is a Consistent estimator of $theta$ then $T^3$ is consistent estimator of $theta^3$
$begingroup$
If T is a Consistent estimator of $theta$ then $T^3$ is a consistent estimator of $theta^3$.
Can anyone tell me in a single line what's the logic behind this? I am familiar with invariance property of MLE where $T$ is MLE of $theta$ and $T^2$ will be MLE of $theta ^2$ and we know that all MLE's are consistent. If there is some other logic please do tell me I might ve skipped that portion. I want to study that.
statistics statistical-inference
asked Dec 12 '18 at 18:18
Daman deepDaman deep
736418
$endgroup$
add a comment |
$begingroup$
If T is a Consistent estimator of $theta$ then $T^3$ is a consistent estimator of $theta^3$.
Can anyone tell me in a single line what's the logic behind this? I am familiar with invariance property of MLE where $T$ is MLE of $theta$ and $T^2$ will be MLE of $theta ^2$ and we know that all MLE's are consistent. If there is some other logic please do tell me I might ve skipped that portion. I want to study that.
statistics statistical-inference
asked Dec 12 '18 at 18:18
Daman deepDaman deep
736418
$endgroup$
2
$begingroup$
Just the usual $a_nto a$ then $a_n^3to a^3$, modified for plim.
$endgroup$
– user10354138
Dec 12 '18 at 18:26
2
$begingroup$
See statement no 2 here.
$endgroup$
– StubbornAtom
Dec 12 '18 at 18:27
1
$begingroup$
@StubbornAtom Bhai you are life saver.
$endgroup$
– Daman deep
Dec 12 '18 at 18:30
add a comment |
$begingroup$
If T is a Consistent estimator of $theta$ then $T^3$ is a consistent estimator of $theta^3$.
Can anyone tell me in a single line what's the logic behind this? I am familiar with invariance property of MLE where $T$ is MLE of $theta$ and $T^2$ will be MLE of $theta ^2$ and we know that all MLE's are consistent. If there is some other logic please do tell me I might ve skipped that portion. I want to study that.
statistics statistical-inference
asked Dec 12 '18 at 18:18
Daman deepDaman deep
736418
$endgroup$
If T is a Consistent estimator of $theta$ then $T^3$ is a consistent estimator of $theta^3$.
Can anyone tell me in a single line what's the logic behind this? I am familiar with invariance property of MLE where $T$ is MLE of $theta$ and $T^2$ will be MLE of $theta ^2$ and we know that all MLE's are consistent. If there is some other logic please do tell me I might ve skipped that portion. I want to study that.
statistics statistical-inference
statistics statistical-inference
asked Dec 12 '18 at 18:18
Daman deepDaman deep
736418
asked Dec 12 '18 at 18:18
Daman deepDaman deep
736418
asked Dec 12 '18 at 18:18
Daman deepDaman deep
736418
asked Dec 12 '18 at 18:18
Daman deepDaman deep
736418
asked Dec 12 '18 at 18:18
Daman deepDaman deep
736418
736418
2
$begingroup$
Just the usual $a_nto a$ then $a_n^3to a^3$, modified for plim.
$endgroup$
– user10354138
Dec 12 '18 at 18:26
2
$begingroup$
See statement no 2 here.
$endgroup$
– StubbornAtom
Dec 12 '18 at 18:27
1
$begingroup$
@StubbornAtom Bhai you are life saver.
$endgroup$
– Daman deep
Dec 12 '18 at 18:30
add a comment |
2
$begingroup$
Just the usual $a_nto a$ then $a_n^3to a^3$, modified for plim.
$endgroup$
– user10354138
Dec 12 '18 at 18:26
2
$begingroup$
See statement no 2 here.
$endgroup$
– StubbornAtom
Dec 12 '18 at 18:27
1
$begingroup$
@StubbornAtom Bhai you are life saver.
$endgroup$
– Daman deep
Dec 12 '18 at 18:30
2
2
$begingroup$
Just the usual $a_nto a$ then $a_n^3to a^3$, modified for plim.
$endgroup$
– user10354138
Dec 12 '18 at 18:26
$begingroup$
Just the usual $a_nto a$ then $a_n^3to a^3$, modified for plim.
$endgroup$
– user10354138
Dec 12 '18 at 18:26
2
2
$begingroup$
See statement no 2 here.
$endgroup$
– StubbornAtom
Dec 12 '18 at 18:27
$begingroup$
See statement no 2 here.
$endgroup$
– StubbornAtom
Dec 12 '18 at 18:27
1
1
$begingroup$
@StubbornAtom Bhai you are life saver.
$endgroup$
– Daman deep
Dec 12 '18 at 18:30
$begingroup$
@StubbornAtom Bhai you are life saver.
$endgroup$
– Daman deep
Dec 12 '18 at 18:30
add a comment |
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2
$begingroup$
Just the usual $a_nto a$ then $a_n^3to a^3$, modified for plim.
$endgroup$
– user10354138
Dec 12 '18 at 18:26
2
$begingroup$
See statement no 2 here.
$endgroup$
– StubbornAtom
Dec 12 '18 at 18:27
1
$begingroup$
@StubbornAtom Bhai you are life saver.
$endgroup$
– Daman deep
Dec 12 '18 at 18:30