Mixing
Is there any relationship between efficiency and correlation coefficient?
$begingroup$
Let $t_1$ be the most efficient estimator and $t_2$ be the less efficient estimator
with efficiency $e$ and let $r$ be correlation coefficient between the two estimator $t_1$ and $t_2$.Define relationship between $e$ and $r$.
So ofcourse $V(t_1)<V(t_2)$
Now I am not sure if $e=dfrac{V(t_1)}{V(t_2)}$ or $e=dfrac{V(t_2)}{V(t_1)}$ because in question it does not say relative efficiency with respect to $t_1$ or $t_2$.
I tried with both of them taking $e=dfrac{V(t_1)}{V(t_2)}$ for now
$r=dfrac{COV(t_1,t_2)}{sqrt{V(t_1)V(t_2)}}$
$ =dfrac{E(t_1t_2)-E(t_1)Et_2)}{{{eV(t_2)}}}$
I am not sure how to proceed now .
statistics statistical-inference estimation correlation
asked Jan 11 at 10:40
Daman deepDaman deep
746418
$endgroup$
add a comment |
$begingroup$
Let $t_1$ be the most efficient estimator and $t_2$ be the less efficient estimator
with efficiency $e$ and let $r$ be correlation coefficient between the two estimator $t_1$ and $t_2$.Define relationship between $e$ and $r$.
So ofcourse $V(t_1)<V(t_2)$
Now I am not sure if $e=dfrac{V(t_1)}{V(t_2)}$ or $e=dfrac{V(t_2)}{V(t_1)}$ because in question it does not say relative efficiency with respect to $t_1$ or $t_2$.
I tried with both of them taking $e=dfrac{V(t_1)}{V(t_2)}$ for now
$r=dfrac{COV(t_1,t_2)}{sqrt{V(t_1)V(t_2)}}$
$ =dfrac{E(t_1t_2)-E(t_1)Et_2)}{{{eV(t_2)}}}$
I am not sure how to proceed now .
statistics statistical-inference estimation correlation
asked Jan 11 at 10:40
Daman deepDaman deep
746418
$endgroup$
$begingroup$
There is a relation if you are looking at the class of unbiased estimators of some function of $theta$, your parameter of interest.
$endgroup$
– StubbornAtom
Jan 11 at 18:30
add a comment |
$begingroup$
Let $t_1$ be the most efficient estimator and $t_2$ be the less efficient estimator
with efficiency $e$ and let $r$ be correlation coefficient between the two estimator $t_1$ and $t_2$.Define relationship between $e$ and $r$.
So ofcourse $V(t_1)<V(t_2)$
Now I am not sure if $e=dfrac{V(t_1)}{V(t_2)}$ or $e=dfrac{V(t_2)}{V(t_1)}$ because in question it does not say relative efficiency with respect to $t_1$ or $t_2$.
I tried with both of them taking $e=dfrac{V(t_1)}{V(t_2)}$ for now
$r=dfrac{COV(t_1,t_2)}{sqrt{V(t_1)V(t_2)}}$
$ =dfrac{E(t_1t_2)-E(t_1)Et_2)}{{{eV(t_2)}}}$
I am not sure how to proceed now .
statistics statistical-inference estimation correlation
asked Jan 11 at 10:40
Daman deepDaman deep
746418
$endgroup$
Let $t_1$ be the most efficient estimator and $t_2$ be the less efficient estimator
with efficiency $e$ and let $r$ be correlation coefficient between the two estimator $t_1$ and $t_2$.Define relationship between $e$ and $r$.
So ofcourse $V(t_1)<V(t_2)$
Now I am not sure if $e=dfrac{V(t_1)}{V(t_2)}$ or $e=dfrac{V(t_2)}{V(t_1)}$ because in question it does not say relative efficiency with respect to $t_1$ or $t_2$.
I tried with both of them taking $e=dfrac{V(t_1)}{V(t_2)}$ for now
$r=dfrac{COV(t_1,t_2)}{sqrt{V(t_1)V(t_2)}}$
$ =dfrac{E(t_1t_2)-E(t_1)Et_2)}{{{eV(t_2)}}}$
I am not sure how to proceed now .
statistics statistical-inference estimation correlation
statistics statistical-inference estimation correlation
asked Jan 11 at 10:40
Daman deepDaman deep
746418
asked Jan 11 at 10:40
Daman deepDaman deep
746418
asked Jan 11 at 10:40
Daman deepDaman deep
746418
asked Jan 11 at 10:40
Daman deepDaman deep
746418
asked Jan 11 at 10:40
Daman deepDaman deep
746418
746418
$begingroup$
There is a relation if you are looking at the class of unbiased estimators of some function of $theta$, your parameter of interest.
$endgroup$
– StubbornAtom
Jan 11 at 18:30
add a comment |
$begingroup$
There is a relation if you are looking at the class of unbiased estimators of some function of $theta$, your parameter of interest.
$endgroup$
– StubbornAtom
Jan 11 at 18:30
$begingroup$
There is a relation if you are looking at the class of unbiased estimators of some function of $theta$, your parameter of interest.
$endgroup$
– StubbornAtom
Jan 11 at 18:30
$begingroup$
There is a relation if you are looking at the class of unbiased estimators of some function of $theta$, your parameter of interest.
$endgroup$
– StubbornAtom
Jan 11 at 18:30
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3069700%2fis-there-any-relationship-between-efficiency-and-correlation-coefficient%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3069700%2fis-there-any-relationship-between-efficiency-and-correlation-coefficient%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
There is a relation if you are looking at the class of unbiased estimators of some function of $theta$, your parameter of interest.
$endgroup$
– StubbornAtom
Jan 11 at 18:30