All Questions
Tagged with likelihood-ratio hypothesis-testing
227
questions
3
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1
answer
55
views
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
0
votes
0
answers
16
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Rejection region in LRT test
Let's say I have $X_i \sim Bi(1, \theta$) and want to test $H_0: \theta \geq \theta_0$ vs $H_1: \theta < \theta_0$.
I've found that $\lambda = \frac{\sup_{\theta \in \Theta_0}L(\theta)}{\sup_{\...
- 101
1
vote
1
answer
56
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Hypothesis Test Finite Sample Spatial Gaussian Mixture Model
I have $n$ observations of pairs $(x, y)$ and three different models I would like to compare. Model0 is nested within Model1. Model0 is also nested within Model2. I would like to do hypothesis ...
- 385
4
votes
1
answer
58
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Likelihood-ratio and score tests of a (non)linear combination of coefficients
The likelihood-ratio and score test are typically used for simple scalar hypotheses such as $\beta_1 = 0$ or $\beta_1 = \beta_2 = 0$. How can we test a linear combination of coefficients using the ...
- 1,824
1
vote
1
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90
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One sided likelihood ratio test for a logistic regression model?
I need to run a one-sided test on one parameter of a logistic regression model:
$H_0$: $\beta = 0$
$H_1$: $\beta \geq 0$
I want to avoid Wald-equivalent methods as these are known to have problems ...
- 939
7
votes
2
answers
105
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LR statistics add up for nested models. What about the Wald test?
Consider models M0, M1, M2.
Let M0 $\subset$ M1 $\subset$ M2, i.e. let the models nest each other.
I test the following pairs of models using the likelihood-ratio (LR) test: M0 vs. M2, M0 vs. M1, M1 ...
- 68.6k
0
votes
0
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14
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How to translate the set of contrasts over model coefficients into definitions of two nested models for Likelihood Ratio testing?
With the data as below:
Categorical predictor: "Group" with 2 levels: Group 1 and Group 2
Categorical predictor: "Treatment" with 3 levels: A, B, C
Categorical binary response: &...
- 11
1
vote
0
answers
34
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How to test specific contrasts about levels of categorical variables through nested models? [closed]
This is not about obtaining any dataset. I HAVE the dataset.
This is not about debugging code, this is about EXPLAINING the way to obtain statistical relationship between the nested models (LRT ANOVA) ...
- 11
3
votes
2
answers
122
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Replicate t or F test from regression using regression likelihoods
I've heard that the t-test and F-test we use to get the significance of our regression results are derived from the likelihood ratio test, but I'm having trouble replicating the p-value of the t/F ...
- 385
5
votes
4
answers
185
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Distribution of $Z^2 \cdot I(Z > 0)$ where $Z \sim \text{N}(0,1)$
When using the Likelihood Ratio test for testing particular hypotheses and attempting to obtain an size-$\alpha$ test, I run into the expression
$$ \mathbb{P}\left( Z^2 \cdot I(Z > 0) > c \right)...
0
votes
1
answer
59
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Constructing a one-sided hypothesis test for joint probabilties of negative binomial distributions
I am conducting research on Codling moth population/trap capture models. The end goal is to have a hypothesis testing model that will provide whether or not (at some significance level $\alpha$) the ...
- 101
0
votes
1
answer
57
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Can I use the ratio of two p-values under two hypotheses as a likelihood ratio?
I am designing a simple study where I ask participants a problem. Then I code the answers as either correct or incorrect. I have a prediction from the literature that the percentage of correct answers ...
- 1
3
votes
1
answer
182
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Karlin-Rubin theorem: relationship between test statistic having the MLR property vs being sufficient
Let's suppose we are trying to compare two hypotheses for a single parameter $\theta$. The null hypothesis $H_0$ is that $\theta = \theta_0$, and the alternative is that $\theta ≥ \theta_0$.
The ...
- 435
6
votes
1
answer
207
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Permutation test for exponential null hypothesis: really bad?
Having found nice formulas for testing the null hypothesis under exponentially-distributed samples, I wanted to see how well permutation tests could do the job. And the answer, assuming no mistakes, ...
- 1,162
1
vote
1
answer
69
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When and why is a likelihood ratio preferable to a difference as a test statistic?
We want to know whether two sample sets {x} and {y} were drawn from the same distribution. The null hypothesis $H_0$ is that they are. As statisticians we test the hypothesis by calculating the p-...
- 1,162