All Questions
Tagged with likelihood-ratio neyman-pearson-lemma
24
questions
3
votes
1
answer
55
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is the likelihood ratio test "best" for finite samples?
Wikipedia says
The Neyman–Pearson lemma states that this likelihood-ratio (lr) test is the most powerful among all level α alpha tests for this case.
Is this only true for infinite sample sizes? Is ...
- 385
1
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0
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54
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UMP two sided tests for exponential families
Consider a random variable $X$ with density $$f(x : θ) = C(θ)e^{η(θ)T(x)}h(x), θ ∈ Θ$$.
Assume that $η(θ)$ is strictly increasing in $θ$ and that the family is full rank. Show that there will not be ...
- 207
1
vote
1
answer
52
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Show a composite test is the most powerful after deriving a similar most powerful simple test
Let $X$ be a real-valued random variable with density $f(x) = (2\theta x + 1 - \theta) \mathbb{1}(x \in [0,1])$ where $1$ here is the indicator function and $-1 < \theta < 1$. I am trying to ...
- 216
1
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1
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118
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Does there always exist for n small, a non-chi-squared test-statistic for the likelihood-ratio (neyman-pearson, karlin-rubin), score, and wald-tests?
An additional reason that the chi-squared distribution is widely used is that it turns up as the large sample distribution of generalized likelihood ratio tests (LRT).[6] LRTs have several desirable ...
user318514
0
votes
0
answers
711
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Which to Use: Likelihood Ratio Test or Uniformly Most Powerful Test?
I've recently been learning about MPTs (most powerful tests), UMPTs (uniformly most powerful tests) and LRTs (likelihood ratio tests), and do not totally understand in which context the different ...
- 55
1
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0
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188
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How to combine two independent likelihood ratio tests?
Let us know that a patient has one of disease A or B. Suppose that we run an experiment to find that the patient has disease A or disease B. The null hypothesis is that the patient has disease A and ...
- 21
0
votes
0
answers
276
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Neyman-Pearson hypothesis testing and composite alternative hypothesis
I am in love with the idea of setting up a statistical test à la Neyman-Pearson when possible, because it is just so intuitive. Most of times, $H_0$ is some kind of point hypothesis, but $H_1$ is ...
- 215
1
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48
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Finding the likelihood ratio to test which distribution has the largest mean
The problem: Let $X_1, \ldots, X_n$ and $Y_1, \ldots, Y_m$ be two i.i.d. samples drawn from $\mathcal{N}(\mu_x, \sigma^2)$ and $\mathcal{N}(\mu_y, \sigma^2)$, respectively. I wanna test $H_0: \mu_x \...
- 66
0
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0
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586
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Proving a test is UMP for Uniformly distributed random variable
Let $X_1, X_2,..., X_n$ be a sample of size n from the PMF
$$P_N(x) = {1 \over N},\ \ \ \ \ \ \ \ \ x = 1,2,...,N;N \in \mathbb{N} $$
Show that
$$
\varphi(x_1, x_2, ..., x_n) = \begin{cases}
1 & ...
- 101
1
vote
1
answer
102
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A basketball probability question using Neyman–Pearson lemma
It is known that the probability of a basketball player to make his first shot is $p=0.6$
A player argues that it does not matter if he made the previous shot or not his odds stays the same. We say if ...
- 113
1
vote
0
answers
133
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Hypothesis testing - Neyman-Pearson Lemma
While studying for my exam and practicing with old exams I came across this question. In the answer to part d) they mention that both coefficients are positive and hence for some c the test in part b) ...
- 11
0
votes
0
answers
287
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Finding UMP test when testing a simple hypothesis against a composite hypothesis
Hi all I have question regarding the following when reading the notes on Page 5 here: http://www.ams.sunysb.edu/~zhu/ams571/Lecture8_571.pdf
The question that I have is when the author showed how to ...
- 649
0
votes
1
answer
310
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Constant value in Neyman Pearson lemma
To know the k value in Neyman Pearson lemma, do we need to know the alternate hypothesis. To what I understood (from articles like PenStateNotes), we could get value of k using null hypothesis and the ...
- 63
1
vote
0
answers
110
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Likelihood ratio test and sample statistics
Given a sample $\mathbf X =(X_1,...,X_n)$ from a parent random variable $X$, Neyman-Pearson's test for two point hypotheses $H_0$ and $H_1$ is the one defined by the critical region
$$C=\left\{\mathbf ...
- 121
9
votes
1
answer
732
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Reproduce figure of "Computer Age Statistical Inference" from Efron and Hastie
The summarized version of my question
(26th December 2018)
I am trying to reproduce Figure 2.2 from Computer Age Statistical Inference by Efron and Hastie, but for some reason that I'm not able to ...
