All Questions
Tagged with likelihood-ratio self-study
63
questions
4
votes
1
answer
100
views
What are the degrees of freedom to consider for a G-test when some cells have expected values of 0?
Let's say I conduct a survey where people can mention their favorite
color among four options (red, green, blue, yellow).
After collecting the data, I create a contingency table crossing
gender with ...
- 57
1
vote
0
answers
35
views
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
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
3
votes
2
answers
304
views
Likelihood ratio test for composite alternative hypothesis
I must admit that my general understanding on how to create critical region to test hypothesis against composite alternative hypothesis is still shaky. Therefore please pardon if my question is too ...
- 871
1
vote
1
answer
916
views
Likelihood ratio test for $H_0: \mu_1 = \mu_2 = 0$ for 2 samples with common but unknown variance
This is a question from Exercises 8.3 from Introduction to Mathematical Statistics by Hogg, Craig, McKean.
Question: Let $X_1, X_2, \cdots ,X_n$ and $Y_1, Y_2, \cdots ,Y_n$ be independent random ...
- 145
1
vote
1
answer
172
views
UMP test for hypergeometric distribution
$P(X=x|N,D,n)=\frac{^DC_x \times ^{(N-D)}C_{(n-x)}}{^NC_n}$
Now, I was trying to test for $H_0:D\le D_0$ vs $H_1:D>D_0$ using likelihood ratio test.
But to find the maximum likelihood estimate of $...
- 37
1
vote
0
answers
444
views
the Wald, Likelihood Ratio (LR) the Lagrange Multiplier (LM) test statistics Are monotonic function of F statistics
Consider a classic linear regression model.
I want to show that the Wald, Likelihood Ratio (LR) the Lagrange Multiplier (LM) test statistics for the null hypothesis $H_0: R\beta =r$ for a constant ...
- 1,140
6
votes
1
answer
3k
views
Likelihood Ratio Test Equivalent with $t$ test: Difference of Two Means from Constant Variance Normal Distributions
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Problem Statement: Suppose that independent random samples of sizes $n_1$ and $n_2$
are to be selected from normal ...
- 5,942
3
votes
2
answers
4k
views
Likelihood Ratio Test for Common Variance from Two Normal Distribution Samples
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Problem Statement: Let $S_1^2$ and $S_2^2$ denote, respectively, the variances of
independent random samples of ...
- 5,942
4
votes
3
answers
2k
views
Binomial Distribution: Likelihood Ratio Test for Equality of Several Proportions
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Problem Statement: A survey of voter sentiment was conducted in four midcity
political wards to compare the fraction ...
- 5,942
4
votes
1
answer
645
views
Convergence rate of log likelihood ratio
I have come across the following statement in the textbook A course on Large Sample Theory by Ferguson - Chapter 17. Strong Consistency of the Maximum Likelihood Estimates.
The likelihood ratio, $L_n(...
- 1,572
2
votes
1
answer
552
views
Likelihood ratio test for two-parameter exponential distribution
I am considering a random sample $X_1, \ldots, X_m; \ m \geq 2$, from a 2-parameter exponential distribution with pdf
$$f_X(x; \mu, \sigma) = \frac{1}{\sigma} \exp \left( -\frac{x-\mu}{\sigma} \right) ...
- 693
4
votes
0
answers
219
views
P-value of LR test
I've been studying more about GLRT (Generalized Likelihood Ratio Tests) and I came up with the following problem.
Let $X\sim N(\theta,1)$ and consider the hypothesis $H_0:\theta\in[a,b]$ against $H_1:\...
6
votes
1
answer
501
views
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
4
votes
1
answer
957
views
How can I show that $\prod^n_{i=1}X_i$ has a monotone likelihood ratio?
We have a random sample $X_1,\cdots,X_n \sim \mathrm{Beta}(\theta,1), \theta > 0$ is unknown. My ultimate goal is to find a UMP size $\alpha$ test for $H_0: \theta \le \theta_0$ v. $H_1: \theta >...
- 2,103