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Aug
21
comment Justify an unbiased estimator is UMVUE
@MichaelHardy I didn't say all. I said that there is also such an option and if so...
Aug
20
comment Justify an unbiased estimator is UMVUE
@MichaelHardy sorry I have a limited inet access. Yes I meant that. For example $X_1,X_2,...\sim \mathrm{i.i.d\,\, Uniform(0},\theta)$, $\hat{\theta}=\max \{X_i\}_{i=1}^n$. This is MLE and the correction is done by multiplying $\hat{\theta}$ by $(n+1)/n$. The latter estimator is UMVUE. It is not MLE but just scaled version of it with some function of the sample size.
Aug
20
comment Reference request for Heine-Borel theorem
@DaveL.Renfro sounds interesting. I checked it here: arxiv.org/pdf/1006.4131.pdf heine-borel theorem is for the real numbers and no closed balls are meant. I was wondering about conclusions for the finite dimensional unit ball "Again from the Heine–Borel theorem, the closed unit ball of any finite-dimensional normed vector space is compact.", here at examples section: en.wikipedia.org/wiki/Compact_space
Aug
20
comment Reference request for Heine-Borel theorem
@hans__ I did already. I cannot find a useful reference there. Otherwise, I wouldnt ask this question..
Aug
20
revised Reference request for Heine-Borel theorem
deleted 2 characters in body; edited tags
Aug
20
comment Reference request for Heine-Borel theorem
sure it does not apply to infinite dimensional spaces. That is why there is quantization as described in the question.
Aug
20
comment Why is $nS_X ^2/\sigma ^2$ $\chi ^2(n-1)$, while the other is $\chi^2(n)$?
it is about what is random and what is not..$\mu$ is not random and $\bar{X}$ is only asymptotically non-random.
Aug
20
asked Reference request for Heine-Borel theorem
Aug
17
comment Justify an unbiased estimator is UMVUE
@MichaelHardy possible. Biased mles can be corrected for the bias and will eventually become unbiased. The question is if there are mles which are not sufficient statistic but they are umvue. I don't believe that there exist such.
Aug
16
comment Justify an unbiased estimator is UMVUE
In principe, a function of every sufficient statistic can be UMVUE. However, It is not sufficient. There are MLEs (a function of the sufficient statistic) which are not UMVUE. The problem is that in such a case it is non-trivial to say if there exists indeed which is UMVUE. My best guess is that UMVUE, if it exists should be a function of sufficient statistic.
Aug
16
comment Justify an unbiased estimator is UMVUE
I havent checked if you derived correclty but if so, then you end up with the roots of a second order polinomial. It seems that the roots must be real because the last term in your equation is positive, i.e. multiply all terms by $-2/n$ and check again. Another thing is that the root is a function of $T$, the last term of you polinomial after normalization by $-2/n$. This suggests, but not proves that $T$ is indeed a sufficient statistic.
Aug
16
comment Justify an unbiased estimator is UMVUE
find the likelihood function then take the logarithm and then find the maximum with respect to the parameter. Write them down in your question as EDIT or ADDED or My work. Then I will tell you more.
Aug
16
comment Justify an unbiased estimator is UMVUE
can you write down the steps you followed to obtain $T$. Intuitively one can expect that the variance of $T$ needs to be less than both the sample mean or sample variance estimator.
Aug
16
comment Distributions, PDFs, and Random Variables in Measure Theory
$f_X$ is the Radon-Nykodym derivative of the probability measure $P$ with respect to a $\sigma-$finitite measure $\mu$, so $f_X$ must be the density function. the measure $\mu$ for the discrete case is the counting measure, so assigns a unit measure to the singletons.
Aug
8
comment Two fundamental questions about convexity of a function (number2)
@MichaelGrant you said that in your example that the saddle value was unique. which point is that? I cannot use the method of partial derivatives. Could you please let me know how we get the point in this case?thx.
Aug
7
comment averaging of multiple curves for signal processing
you can average the signals are you average the numbers. In Matlab: $V_1=V_2+V_3$, the sizes of the vectors must be the same. If the some of the signals are more important, then you may want to weight it differently before summing up.
Aug
7
comment averaging of multiple curves for signal processing
you can put the image here just. Go to edit and use the icon above which appears as an image.
Aug
7
comment Why are these two sigma algebras independent?
what is $P(E)\cap P(Q)$?
Aug
7
comment averaging of multiple curves for signal processing
you may want to give more details about your question. what average curve are you talking about. why not taking the average of all 5 curves?
Aug
1
comment What does it mean to be $0.9-$Dimension?
how about "what does it mean to be a non-integer dimension"