Trace of disturbance vector squared
$begingroup$
I was reading Jushan Bai's paper (2009) and came across the least squares objective function is as follows: tr[(W-FA')(W-FA')'] from W = FA'+ e on page 1236.
I am sorry about my notation since I do not know how
to write Greek letters here (A should be like Lamda)
That function seems strange to me since the residual sum of squares would be the choice for the function for me and I see if he considered RSS, RSS could be written as tr(W'MfW) on the next line on the paper, where Mf is the projection matrix.
But his objective function considers the squared disturbance and there, I don't even understand why the transpose mark is attached like ee', not like e'e
which is more similar to RSS, I guess...
Could please anyone help me with this?
Thanks a lot in advance.
statistics
asked Dec 18 '18 at 5:05
June ParkJune Park
11
$endgroup$
add a comment |
$begingroup$
I was reading Jushan Bai's paper (2009) and came across the least squares objective function is as follows: tr[(W-FA')(W-FA')'] from W = FA'+ e on page 1236.
I am sorry about my notation since I do not know how
to write Greek letters here (A should be like Lamda)
That function seems strange to me since the residual sum of squares would be the choice for the function for me and I see if he considered RSS, RSS could be written as tr(W'MfW) on the next line on the paper, where Mf is the projection matrix.
But his objective function considers the squared disturbance and there, I don't even understand why the transpose mark is attached like ee', not like e'e
which is more similar to RSS, I guess...
Could please anyone help me with this?
Thanks a lot in advance.
statistics
asked Dec 18 '18 at 5:05
June ParkJune Park
11
$endgroup$
$begingroup$
A brief introduction to posting mathematical notation may be of interest to you. It has links to more detailed information.
$endgroup$
– hardmath
Dec 18 '18 at 5:35
add a comment |
$begingroup$
I was reading Jushan Bai's paper (2009) and came across the least squares objective function is as follows: tr[(W-FA')(W-FA')'] from W = FA'+ e on page 1236.
I am sorry about my notation since I do not know how
to write Greek letters here (A should be like Lamda)
That function seems strange to me since the residual sum of squares would be the choice for the function for me and I see if he considered RSS, RSS could be written as tr(W'MfW) on the next line on the paper, where Mf is the projection matrix.
But his objective function considers the squared disturbance and there, I don't even understand why the transpose mark is attached like ee', not like e'e
which is more similar to RSS, I guess...
Could please anyone help me with this?
Thanks a lot in advance.
statistics
asked Dec 18 '18 at 5:05
June ParkJune Park
11
$endgroup$
I was reading Jushan Bai's paper (2009) and came across the least squares objective function is as follows: tr[(W-FA')(W-FA')'] from W = FA'+ e on page 1236.
I am sorry about my notation since I do not know how
to write Greek letters here (A should be like Lamda)
That function seems strange to me since the residual sum of squares would be the choice for the function for me and I see if he considered RSS, RSS could be written as tr(W'MfW) on the next line on the paper, where Mf is the projection matrix.
But his objective function considers the squared disturbance and there, I don't even understand why the transpose mark is attached like ee', not like e'e
which is more similar to RSS, I guess...
Could please anyone help me with this?
Thanks a lot in advance.
statistics
statistics
asked Dec 18 '18 at 5:05
June ParkJune Park
11
asked Dec 18 '18 at 5:05
June ParkJune Park
11
asked Dec 18 '18 at 5:05
June ParkJune Park
11
asked Dec 18 '18 at 5:05
June ParkJune Park
11
asked Dec 18 '18 at 5:05
June ParkJune Park
11
11
$begingroup$
A brief introduction to posting mathematical notation may be of interest to you. It has links to more detailed information.
$endgroup$
– hardmath
Dec 18 '18 at 5:35
add a comment |
$begingroup$
A brief introduction to posting mathematical notation may be of interest to you. It has links to more detailed information.
$endgroup$
– hardmath
Dec 18 '18 at 5:35
$begingroup$
A brief introduction to posting mathematical notation may be of interest to you. It has links to more detailed information.
$endgroup$
– hardmath
Dec 18 '18 at 5:35
$begingroup$
A brief introduction to posting mathematical notation may be of interest to you. It has links to more detailed information.
$endgroup$
– hardmath
Dec 18 '18 at 5:35
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%2f3044791%2ftrace-of-disturbance-vector-squared%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%2f3044791%2ftrace-of-disturbance-vector-squared%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
$begingroup$
A brief introduction to posting mathematical notation may be of interest to you. It has links to more detailed information.
$endgroup$
– hardmath
Dec 18 '18 at 5:35