All Questions
Tagged with likelihood-ratio inference
26
questions
0
votes
0
answers
39
views
Likelihood ratios not distributed as a chi2 distribution with the correct dof (Wilks' theorem)
I perform Bayesian inference on a mixture model such that $\mu$ is the mixture weight for a feature in the mixture
$p(x | \mu, \theta) = \mu p_{f}(x|\theta) + (1-\mu)p_{nf}(x|\theta)$
I have prior $p(\...
5
votes
1
answer
110
views
Does performing Likelihood Ratio Test to compare two nested LASSO models make statistical sense?
From what I've studied, the LRT is used to compare two nested models, i.e. 2 models having different sets of nested features, in my case e.g.
Model1: binary_outcome ~ X1 + X2
Model2: binary_outcome ~ ...
- 53
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
1
vote
0
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35
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Generalized likelihood ratio test for a left-truncated exponential distribution [duplicate]
I am doing self study in statistical inference and am rather confused about how to approach generalized likelihood ratio test (GLRT) problems. I am trying the traditional approach by definition and ...
- 160
0
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0
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170
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Null model is a better fit for the data compared to experimental model?
I have built a generalised linear mixed effects model fitted to a gamma distribution. I am wanting to compare this experimental model to a nested null model to see whether it is a better fit for the ...
2
votes
1
answer
66
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Likelihood ratio test for model specification with boundary Null
I am interested in understanding the asymptotic distribution of Likelihood ratio (LR) test statistic for model specification. I am focusing on the case in which the null hypothesis is of the form (i.e....
- 21
5
votes
2
answers
847
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Is the Likelihood Ratio test using cluster robust standard errors fixable by Bootstrap (or someting else)?
There is a common agreement about the invalidity of using likelihood ratio tests when computing Maximum Likelihood Estimates (MLE) using clustered corrected standard errors. The main argument is that ...
- 229
6
votes
1
answer
501
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Likelihood ratio test for $H_0:(\mu_1,\mu_2)=(0,0)$ vs $H_1:(\mu_1,\mu_2) \neq (0,0)$
There are $X_1, X_2$ where $X_i \sim N(\mu_i,1), i=1,2$. They are independent. The question is
Find the likelihood ratio test with $H_0:(\mu_1,\mu_2)=(0,0), H_1:(\mu_1,\mu_2) \neq (0,0)$. The ...
- 478
8
votes
1
answer
2k
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Understanding how to find more "extreme" values when calculating p values in two sided hypothesis tests
In hypothesis testing, the definition of p value is the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is ...
user279822
0
votes
0
answers
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
4
votes
1
answer
943
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Chi square approximation of the likelihood test ratio
I wasn't able to find any satisfying answer about that topic. I hope someone who understand correctly the subject could enlighten this shadow.
This is not very important, just for the sake of ...
- 333
1
vote
0
answers
23
views
Find the Rejection Region using the Likelyhood Quotient
H0:= l=8, Ha:= l=10
from a random sample of N=9
where f(xi)=l*exp(-lxi) and a=0.05
Find the Rejection Region, please help
I think i get confused when getting the likelyhood quotient because i ...
- 11
1
vote
0
answers
174
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Likelihood ratio test and critical region
I'm not really understanding some theoretical passages about the LRT used for composite hypothesis test.
I know that the LRT
$\lambda_{01}(x_n)=\frac{sup_{\Theta_0}L(\theta;x_n)}{sup_{\Theta}L(\...
- 61
1
vote
1
answer
619
views
Generalized likelihood ratio in uniform distribution
My question is to come up with the form of the GLR when testing the following:
Let $X_1,\ldots, X_n$ be a random sample from a distribution with pdf $f(x;\theta,\mu) = \frac{1}{2\theta}$ if $|x-\mu|...
- 649
1
vote
0
answers
242
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Asymptotic Distribution of Wald test
If $X_1 , X_2 , ... X_n$ are iid and they have the same pdf $f_θ(x)$ .
Consider testing $H_0 : θ= θ_0$ vs $H_n : θ = θ_0 +Δ * n^{-1/2}$.
where , $Δ = (Δ_1 , Δ_2 , .. Δ_k)^T$
We want to find the ...
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