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 Yearling
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2d
comment Testing the Uniformly Most Powerful Test against the alternative
What about Short for Karlin Rubin Theorem?
2d
comment Testing the Uniformly Most Powerful Test against the alternative
that sounds good. lets say we choose NP lemma, how should we apply it here to see if there is a UMP test? do you think that KRT can directly be applied here?
2d
comment Testing the Uniformly Most Powerful Test against the alternative
do you know what is UMP test? and how to check for that?
Apr
25
awarded  Yearling
Apr
24
comment Sample Variance Divided by Sample Size?
They are basically the statistics of a sample mean estimator.
Apr
1
comment How does one calculate the expected value?
Please useTex to type for your next post.
Apr
1
revised How does one calculate the expected value?
added 16 characters in body; edited title
Mar
31
comment Optimization of a tabulation under constraint
in your example why not $A=(2,1;2,4)$ or why not $A=(1,1.0001;2,4)$?
Mar
25
comment What is the physical meaning of 'infinite variance'?
yes there is a reason: "standard Cauchy distribution" does not have an infinite variance.
Mar
15
comment Average probability problem
have you ever heart about Bernoulli distribution?
Mar
9
comment Is the given binomial sum almost everywhere negative as $K\to\infty$?
The difference for even $K$ is that for $\theta$ very close to $1/2$ from left, one needs so huge $K$ to get sth. negative but this is not the case for odd $K$. Both odd and even $K$ converge to the same pattern eventually, and it is also normal that one doesnt see this in the proof (and actually it is also not necessary).
Mar
9
comment Is my optimization model correct
I dont know if your optimization model is correct or not since the question is quite long to read. But I am certainly sure that the photo in your profile reflects a model for which no optimizations is required.
Mar
6
comment Solution in terms of singular values and singular vectors
Let $U S V^T:=V\Sigma^2V^T$. Apply your formula to $U S V^T$ and at the end replace with $V\Sigma^2V^T$. So $U S V^T=\sum \sigma_i^2 u_i v_i^T$, and here the diagonal elements of $S$ are then $\sigma_i^2$...
Mar
6
comment Solution in terms of singular values and singular vectors
if I am not mistaken the first term is $\sum \sigma_i^2 I$. Then one divides both sides by $\sum \sigma_i^2+\alpha^2$.
Mar
3
comment Expectation of log likelihood ratio
Isn't it another density with another parameter? So the maximum likelihood will go to the true parameter as n goes to infinity. As a result there will be another density.
Mar
2
comment Expectation of log likelihood ratio
the integral is the KL divergence, which is always positive, so the whole term should be negative
Feb
26
comment Is the given binomial sum almost everywhere negative as $K\to\infty$?
thank Byron, good idea!
Feb
26
accepted Is the given binomial sum almost everywhere negative as $K\to\infty$?
Feb
25
comment Flipping fair coin -
or even three! there is 3 $-\sigma$ rejection rule.
Feb
24
comment Is $f$ a probability density function?
It is true. The reason is due to the measure theoretic definition of the density function. In this case probably one needs to find the integral as $F(\infty)-F(a)=1-F(a)=P(X\geq a)$