All Questions
Tagged with likelihood-ratio maximum-likelihood
94
questions
0
votes
0
answers
16
views
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
3
votes
1
answer
94
views
likelihood ratio tests on bounded parameters
I am confused by the likelihood ratio test's boundary condition limitation. A commonly stated is that it causes problem for variance parameter because it is bounded below by 0. Can these models ...
- 1,694
2
votes
1
answer
52
views
equivalence between the likelihood ratio test and t-tests
The linked sites (link1, link2) demonstrate that the likelihood ratio tests and the corresponding one- and two-sample t-tests are equivalent. However, based on my understanding, the null distribution ...
- 1,694
4
votes
1
answer
89
views
Does the "log-likelihood" measure cover all details about model fit, like covariance structure, adjustments, robust variance estimator, etc?
Just a general statistical question: when any statistical software returns log-likelihood of some model, does it account for all details in it?
For example, when we employ generalized least square ...
- 51
1
vote
0
answers
61
views
Exact Likelihood ratio statistic for discrete distribution
Suppose that the random variables in a sample $Y_1, Y_2, \ldots, Y_n$ are iid with values in $[0,1]$, and that an investigator knows that the underlying probability density $f_Y(y)$ has the form
$f_Y(...
- 133
1
vote
0
answers
93
views
What is the influence of multicolinearity on the likelihood ratio test?
I learned the two concepts separately and I try to find out how these concepts relate to each other.
To illustrate the question introduce three models. The models establish a relation between age (AGE)...
- 273
0
votes
0
answers
146
views
Proof Maximum likelihood ratio test to be a $\chi^2$ distribution
I have been struggling with this demonstration and I can not finish it, I want to demonstrate that for Gaussian samples (of $\sigma$ and $\mu$) the maximum likelihood ratio test holds for a $\chi^2$ ...
- 123
7
votes
1
answer
93
views
Why not always use CI's from LRT since they don't require symmetry?
I'm confused on why anyone would appeal to asymptotic normality of mle,
$$\hat{\theta} - \theta_0 \rightarrow^D N(0,I^{-1}(\theta))$$
When we can simply invert the likelihood ratio test
$$L(\hat{\...
- 151
1
vote
1
answer
558
views
GLRT of exponential distribution and critical region
Find the Generalized likelihood ratio test (GLRT) for $H_0: \lambda = \lambda_0$ when $H_A: \lambda \ne \lambda_0$ for $X_1 ... X_n$ taken from $X \sim Exp(\lambda;x)$, with a test size of $0.06$, ...
- 131
1
vote
1
answer
357
views
Likelihood Ratio Test for Bivariate Normal in a Restricted Parameter Space
Let $(X_{1i},X_{2i})$ follow a bivariate normal distribution for $i=1,\dots,n$ with means $(\theta_1,\theta_2)$ and an identity variance matrix. Suppose that the parameter space is restricted to $\...
0
votes
0
answers
213
views
Generalized likelihood ratio test for known means and unknown variance
Consider a sequence, $X_1, X_2, \dots, X_n$, of independent random variables. I have two hypotheses:
$H_0 : X_k \sim \mathcal{N}(\mu_0, \sigma^2), k=1,2,\dots,n$
$H_1 : X_k \sim \mathcal{N}(\mu_1, \...
- 1
5
votes
2
answers
847
views
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
0
votes
0
answers
247
views
Likelihood Ratio Test without Chi-square test
Likelihood ratio test (LRT) usually uses a chi-square test to compare two different models.
Are there any variants of LRT that does not use chi-square test?
- 823
0
votes
0
answers
311
views
likelihood ratio test for three variables
I believe my question is similar with this one:
Likelihood-ratio test for three models?
But I do still not understand and my problem is slightly different (maybe). I want to check which model is best, ...
- 11
0
votes
0
answers
31
views
Interprete AIC as significance test and determine significance level for nested models
Let's say we have two nested models.
The smaller one (corresponds to $H_0$) has $p_0$ parameters, so its AIC is given by $$AIC_0=-2\log L_0+2p_0$$
The larger model has $p_1:=p_0+d$ parameters of which ...
- 101