All Questions
Tagged with optimal hypothesis-testing
9 questions
0
votes
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25
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Unbiased test for homogeneity of means of exponenential samples
Given $K$ independent samples of $Y_{i1},\dots,Y_{in_i} \ \text{i.i.d.} \ \sim Exp(\lambda_i)$ with $i=1,\dots, K$ and $n_i$ the size of the $i$-th sample, is there any statistics with analytically ...
- 82.8k
1
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0
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69
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UMP two sided tests for exponential families
Consider a random variable $X$ with density $$f(x : θ) = C(θ)e^{η(θ)T(x)}h(x), θ ∈ Θ$$.
Assume that $η(θ)$ is strictly increasing in $θ$ and that the family is full rank. Show that there will not be ...
- 82.8k
2
votes
1
answer
700
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UMP test and non-decreasing power function
Let $\phi$ be a UMP test for $H_o: \theta \leq \theta_0$ and $H_1: \theta > \theta_0$. Let its power function, $E_\theta(\phi)$, be differentiable w.r.t. $\theta$.
Show the power function is non-...
- 11.6k
2
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1
answer
243
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Most powerful test for Hardy–Weinberg proportions
Consider a population with three kinds of individuals labeled $1, 2$, and $3$ occuring in the Hardy–Weinberg proportions $f(1,\theta)=\theta^2,f(2,\theta)=2\theta(1−\theta),f(3,\theta)=(1−\theta)^2$. ...
- 9,001
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1
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1k
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Uniformly most powerful test does not exists
I am having tough time understanding this concept
The book says:
“We caution the reader that UMP tests for testing H0 : θ1 ≤ θ ≤ θ2 and
H0′ : θ = θ0 for the one-parameter exponential family do not ...
- 46.8k
1
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62
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What is the best algorithm so far for probabilistic adaptive group testing?
I am checking https://en.wikipedia.org/wiki/Group_testing#Classification_of_group-testing_problems but could not figure out the answer.
I am focusing on probabilistic adaptive group testing. The ...
- 82.8k
2
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104
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A test for a binomial r.v. vs. sum of two binomial r.v.'s?
Suppose I draw a sample from one of the two possible random variables $X$ or $Y$ where $X\sim\text{Binomial}(p,N)$ and $Y=A+B$ with $A\sim\text{Binomial}(p,M)$ and $B\sim\text{Binomial}(q,N-M)$. ...
- 82.8k
1
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0
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121
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What parameter to use when testing a SVM classifier on an independent test dataset?
I am trying to make a classifier that effectively distinguishes between control group and patient group, and then I want to use that classifier to distinguish high-risk patients who convert to patient ...
- 107k
6
votes
2
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864
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Drawing numbered balls from an urn
PROBLEM
There is an urn with a set of balls where each ball is labeled with a different integer. The numbers on the balls are known and are not a range of integers. For example the set of balls could ...
- 7,262