Seyhmus Güngören
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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 $F(\infty)-F(a)=1-F(a)=P(X\geq a)$