Neyman-Pearson lemma with pdf of $X$ vs Neyman-Pearson Lemma with likelihood functions
As written in the subject line, I’m confused about the statement made in the Neyman-Pearson Lemma, largely because one of my two textbooks states the Lemma in terms of the pdf of $X$ while the other textbook states the Lemma in terms of the likelihood function of $X$. I don’t believe that the two statements are logically equivalent. Any thoughts on this discrepancy?
statistics statistical-inference hypothesis-testing
asked Nov 28 '18 at 16:52
DavidSDavidS
337111
add a comment |
As written in the subject line, I’m confused about the statement made in the Neyman-Pearson Lemma, largely because one of my two textbooks states the Lemma in terms of the pdf of $X$ while the other textbook states the Lemma in terms of the likelihood function of $X$. I don’t believe that the two statements are logically equivalent. Any thoughts on this discrepancy?
statistics statistical-inference hypothesis-testing
asked Nov 28 '18 at 16:52
DavidSDavidS
337111
If you have a sample $X=(X_1,ldots,X_n)$, then it is the joint density of $(X_1,ldots,X_n)$ (likelihood function) and if you have a single observation $X$ (i.e. for $n=1$), then it is the pdf of $X$. What's the difference?
– StubbornAtom
Nov 29 '18 at 15:46
add a comment |
As written in the subject line, I’m confused about the statement made in the Neyman-Pearson Lemma, largely because one of my two textbooks states the Lemma in terms of the pdf of $X$ while the other textbook states the Lemma in terms of the likelihood function of $X$. I don’t believe that the two statements are logically equivalent. Any thoughts on this discrepancy?
statistics statistical-inference hypothesis-testing
asked Nov 28 '18 at 16:52
DavidSDavidS
337111
As written in the subject line, I’m confused about the statement made in the Neyman-Pearson Lemma, largely because one of my two textbooks states the Lemma in terms of the pdf of $X$ while the other textbook states the Lemma in terms of the likelihood function of $X$. I don’t believe that the two statements are logically equivalent. Any thoughts on this discrepancy?
statistics statistical-inference hypothesis-testing
statistics statistical-inference hypothesis-testing
asked Nov 28 '18 at 16:52
DavidSDavidS
337111
asked Nov 28 '18 at 16:52
DavidSDavidS
337111
asked Nov 28 '18 at 16:52
DavidSDavidS
337111
asked Nov 28 '18 at 16:52
DavidSDavidS
337111
asked Nov 28 '18 at 16:52
DavidSDavidS
337111
337111
If you have a sample $X=(X_1,ldots,X_n)$, then it is the joint density of $(X_1,ldots,X_n)$ (likelihood function) and if you have a single observation $X$ (i.e. for $n=1$), then it is the pdf of $X$. What's the difference?
– StubbornAtom
Nov 29 '18 at 15:46
add a comment |
If you have a sample $X=(X_1,ldots,X_n)$, then it is the joint density of $(X_1,ldots,X_n)$ (likelihood function) and if you have a single observation $X$ (i.e. for $n=1$), then it is the pdf of $X$. What's the difference?
– StubbornAtom
Nov 29 '18 at 15:46
If you have a sample $X=(X_1,ldots,X_n)$, then it is the joint density of $(X_1,ldots,X_n)$ (likelihood function) and if you have a single observation $X$ (i.e. for $n=1$), then it is the pdf of $X$. What's the difference?
– StubbornAtom
Nov 29 '18 at 15:46
If you have a sample $X=(X_1,ldots,X_n)$, then it is the joint density of $(X_1,ldots,X_n)$ (likelihood function) and if you have a single observation $X$ (i.e. for $n=1$), then it is the pdf of $X$. What's the difference?
– StubbornAtom
Nov 29 '18 at 15:46
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%2f3017371%2fneyman-pearson-lemma-with-pdf-of-x-vs-neyman-pearson-lemma-with-likelihood-fun%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%2f3017371%2fneyman-pearson-lemma-with-pdf-of-x-vs-neyman-pearson-lemma-with-likelihood-fun%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
If you have a sample $X=(X_1,ldots,X_n)$, then it is the joint density of $(X_1,ldots,X_n)$ (likelihood function) and if you have a single observation $X$ (i.e. for $n=1$), then it is the pdf of $X$. What's the difference?
– StubbornAtom
Nov 29 '18 at 15:46