All Questions
Tagged with likelihood-ratio distributions
21
questions
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)...
3
votes
1
answer
180
views
Likelihood Ratio Testing for Binomial Distributions
I have a feeling this is a silly question. I am working on a research paper, at some point in it we perform a likelihood ratio test. The first guess would be to apply Wilks's theorem. However, if we ...
1
vote
1
answer
99
views
Likelihood that observed relative frequencies match a probability distribution
For this question, please assume probability distributions are discrete.
If I have $N$ data points ($x_1, x_2, ..., x_N$), and I want to know the likelihood that these samples came from a discrete ...
- 213
4
votes
1
answer
651
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Intuition for Wilks' theorem
I'm trying to wrap my head around why it is intuitive that (under certain conditions) the likelihood ratio statistic follows a chi-squared distribution, asymptotically.
I've looked at the excellent ...
- 43
5
votes
1
answer
362
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Distributions fitting, a comparison
I tried to make a comparison among various candidate distributions fitting for my data. These data are daily returns of S&P500 US equity Index. Among others I tried with t-location-scale (https://...
- 5,729
0
votes
0
answers
22
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Do I need any further assumption to derive the distribution of likelihood ratio
So I am trying to derive the distribution of likelihood ratio, $\Lambda$ under a given hypothesis $H_0$.
But all I'm given is that $Pr(\Lambda \geq x | H_0) = 1/x$. I cant help but feel that the ...
- 101
3
votes
2
answers
3k
views
Multivariate normal distribution - hypothesis testing MLE
Suppose $X_{1}, X_{2},\ldots,X_{n}$ are i.i.d. observations from a multivariate normal distribution $N(\mu,\Sigma)$ where $\Sigma$ is known.
Use the likelihood ratio procedure to produce a test ...
- 31
2
votes
0
answers
221
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Choosing between two normal distributions
I have two normal distributions with different means and variances:
N(u1, s1)
N(u2, s2)
And I have some data points (X) that were sampled from each of them. For each data point, I want to calculate ...
- 191
1
vote
0
answers
233
views
Test for significant difference in ratios of sample means
I have the same scenario here: Test for significant difference in ratios of normally distributed random variables
Suppose I have to compare a metric that is a ratio of two sample means for men and ...
- 43
2
votes
1
answer
216
views
Likelihood ratio test for non-Gaussian distributions
I am learning about the likelihood ratio test. Is the LRT applicable for non-Gaussian distributions too? Up to now I have only been able to find examples of the LRT for Gaussian and Gaussian mixture ...
- 175
2
votes
0
answers
557
views
Q: Determine the Rejection Region of LRT for two Uniform Distributed Samples
Assume we have two independent random samples $(X_i)_{i=1}^{n}$ and $(Y_i)_{i=1}^{m}$ where $X_i\sim\mathrm{Uniform}(0,\theta_1)$ and $Y_j\sim\mathrm{Uniform}(0,\theta_2)$. To test, at the significant ...
- 136
3
votes
1
answer
148
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Why Likelihood function not exactly maximized at the obtained estimate? (R code provided)
Background:
Suppose I have a parameter called "$d$" that is linearly related to the non-centrality parameter ($ncp$) of a $t~distribution$. Specifically,
(1) $ncp = d\sqrt(n)$. And ...
- 4,076
2
votes
1
answer
65
views
How can I determine the distribution of a statistic?
A similar question has been asked, but no answer was posted, so here I am again.
I was doing a Likelihood ratio test and it yielded an ugly expression. Take this example: if $X$ is $B(n,p)$ ...
- 902
6
votes
2
answers
2k
views
Can I use likelihood-ratio test to compare two samples drawn from power-law distributions?
I have to compare two large samples ($N = 10^{6}$) of discrete data drawn from power-law distributions to assess whether they are significantly different. I can't do that by means of a two-sample ...
- 5,126
6
votes
1
answer
919
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Question about Dynkin Lehmann Scheffe Theorem
I'm self-studying for an examination, and I would like to understand how to use the Dynkin Lehmann Scheffe theorem for an applied question.
I am using Bickel and Doksum's "Mathematical Statistics" (...
- 61