What effects the estimation of a sample covariance matrix?
If I have some data recorded at a sampling rate, $F_s$, from $N$ different sensors attached to some hypothetical experiment. Each signal lasts $T$ seconds. I subtract each of the means from each of the respective signals.
I want to know the spatial covariance matrix of my recording/experimental subject. I can build the Sample covariance matrix.
My question is, what effects the accuracy of this covariance matrix estimation?
For example if my sampling rate is low, I have a small number of data points in $T$. I presume this is bad for estimating the covariance matrix, and so would expect the accuracy of this estimation to increase as I increase the sampling rate $F_s$.
I have read somewhere that increasing $N$, my number of sensors and thereby the dimension of the covariance matrix, would reduce this accuracy (apparently due to more samples needed to build non singular covariance matrices - but my knowledge isn't enough to understand why this is important).
Could this problem be solved by increasing the sampling rate? What if the signal I'm recording has an oscillatory frequency less than that of the sampling rate? Will adding extra datapoints in the signal improve the estimation - even if there is technically no new information in the signal?
signal-processing covariance
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
asked Dec 3 '18 at 14:17
bidby
876
add a comment |
If I have some data recorded at a sampling rate, $F_s$, from $N$ different sensors attached to some hypothetical experiment. Each signal lasts $T$ seconds. I subtract each of the means from each of the respective signals.
I want to know the spatial covariance matrix of my recording/experimental subject. I can build the Sample covariance matrix.
My question is, what effects the accuracy of this covariance matrix estimation?
For example if my sampling rate is low, I have a small number of data points in $T$. I presume this is bad for estimating the covariance matrix, and so would expect the accuracy of this estimation to increase as I increase the sampling rate $F_s$.
I have read somewhere that increasing $N$, my number of sensors and thereby the dimension of the covariance matrix, would reduce this accuracy (apparently due to more samples needed to build non singular covariance matrices - but my knowledge isn't enough to understand why this is important).
Could this problem be solved by increasing the sampling rate? What if the signal I'm recording has an oscillatory frequency less than that of the sampling rate? Will adding extra datapoints in the signal improve the estimation - even if there is technically no new information in the signal?
signal-processing covariance
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
asked Dec 3 '18 at 14:17
bidby
876
add a comment |
If I have some data recorded at a sampling rate, $F_s$, from $N$ different sensors attached to some hypothetical experiment. Each signal lasts $T$ seconds. I subtract each of the means from each of the respective signals.
I want to know the spatial covariance matrix of my recording/experimental subject. I can build the Sample covariance matrix.
My question is, what effects the accuracy of this covariance matrix estimation?
For example if my sampling rate is low, I have a small number of data points in $T$. I presume this is bad for estimating the covariance matrix, and so would expect the accuracy of this estimation to increase as I increase the sampling rate $F_s$.
I have read somewhere that increasing $N$, my number of sensors and thereby the dimension of the covariance matrix, would reduce this accuracy (apparently due to more samples needed to build non singular covariance matrices - but my knowledge isn't enough to understand why this is important).
Could this problem be solved by increasing the sampling rate? What if the signal I'm recording has an oscillatory frequency less than that of the sampling rate? Will adding extra datapoints in the signal improve the estimation - even if there is technically no new information in the signal?
signal-processing covariance
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
asked Dec 3 '18 at 14:17
bidby
876
If I have some data recorded at a sampling rate, $F_s$, from $N$ different sensors attached to some hypothetical experiment. Each signal lasts $T$ seconds. I subtract each of the means from each of the respective signals.
I want to know the spatial covariance matrix of my recording/experimental subject. I can build the Sample covariance matrix.
My question is, what effects the accuracy of this covariance matrix estimation?
For example if my sampling rate is low, I have a small number of data points in $T$. I presume this is bad for estimating the covariance matrix, and so would expect the accuracy of this estimation to increase as I increase the sampling rate $F_s$.
I have read somewhere that increasing $N$, my number of sensors and thereby the dimension of the covariance matrix, would reduce this accuracy (apparently due to more samples needed to build non singular covariance matrices - but my knowledge isn't enough to understand why this is important).
Could this problem be solved by increasing the sampling rate? What if the signal I'm recording has an oscillatory frequency less than that of the sampling rate? Will adding extra datapoints in the signal improve the estimation - even if there is technically no new information in the signal?
signal-processing covariance
signal-processing covariance
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
asked Dec 3 '18 at 14:17
bidby
876
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
asked Dec 3 '18 at 14:17
bidby
876
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
edited Dec 3 '18 at 16:17
Tianlalu
3,09621038
3,09621038
asked Dec 3 '18 at 14:17
bidby
876
asked Dec 3 '18 at 14:17
bidby
876
asked Dec 3 '18 at 14:17
bidby
876
876
add a comment |
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%2f3024108%2fwhat-effects-the-estimation-of-a-sample-covariance-matrix%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.
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%2f3024108%2fwhat-effects-the-estimation-of-a-sample-covariance-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
