Two dimensional Linear Regression Hat Matrix
Let X=(X1, X2)nxp where X1 (nxq) with rank=q and X2 (nx(p-q)) with rank=(p-q).
Let H and H1 be hat matrix of X and X1.
1) Prove that HH1=H1 and H1H=H1
2) Prove that (H-H1) is idempotent
matrices statistics linear-regression
asked Dec 9 '18 at 19:54
maari
1
add a comment |
Let X=(X1, X2)nxp where X1 (nxq) with rank=q and X2 (nx(p-q)) with rank=(p-q).
Let H and H1 be hat matrix of X and X1.
1) Prove that HH1=H1 and H1H=H1
2) Prove that (H-H1) is idempotent
matrices statistics linear-regression
asked Dec 9 '18 at 19:54
maari
1
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
– postmortes
Dec 9 '18 at 19:56
add a comment |
Let X=(X1, X2)nxp where X1 (nxq) with rank=q and X2 (nx(p-q)) with rank=(p-q).
Let H and H1 be hat matrix of X and X1.
1) Prove that HH1=H1 and H1H=H1
2) Prove that (H-H1) is idempotent
matrices statistics linear-regression
asked Dec 9 '18 at 19:54
maari
1
Let X=(X1, X2)nxp where X1 (nxq) with rank=q and X2 (nx(p-q)) with rank=(p-q).
Let H and H1 be hat matrix of X and X1.
1) Prove that HH1=H1 and H1H=H1
2) Prove that (H-H1) is idempotent
matrices statistics linear-regression
matrices statistics linear-regression
asked Dec 9 '18 at 19:54
maari
1
asked Dec 9 '18 at 19:54
maari
1
asked Dec 9 '18 at 19:54
maari
1
asked Dec 9 '18 at 19:54
maari
1
asked Dec 9 '18 at 19:54
maari
1
1
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
– postmortes
Dec 9 '18 at 19:56
add a comment |
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
– postmortes
Dec 9 '18 at 19:56
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
– postmortes
Dec 9 '18 at 19:56
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
– postmortes
Dec 9 '18 at 19:56
add a comment |
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%2f3032889%2ftwo-dimensional-linear-regression-hat-matrix%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3032889%2ftwo-dimensional-linear-regression-hat-matrix%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
Try to format this using MathJax, as at the moment it's hard to understand what your notation means. It's also a good idea to show what you've attempted as knowing where you're stuck can help produce good answers.
– postmortes
Dec 9 '18 at 19:56