The proof tag has no wiki summary.
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Question about proof for luce choice axiom w.r.t. conditional probability
In Luce (1959) the choice axiom is definied, that for a finite subset $T$ of $U$ such that, for every $S\subset T, P_S$ is defined.
If $P(x,y)\ne 0,1$ for all $x,y\in T$, then for $R\subset S\subset ...
2
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1answer
32 views
Proof of a PD covariance matrix for conditional Gaussian
I was looking at the formula for the conditional covariance of a partitioned matrix. I understand the intuition behind the equation for the conditional covariance, but I'm not sure how to show that ...
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0answers
10 views
Conditions for the existence of UMP in one-sided two sample hypothesis test
Assume that there are two samples from, possibly, two distinct distributions.
I would like to find a UMP test $H_0: p_1 = p_2 = x$ versus $H_1: x < p_1 < p_2$. If that is not possible, I would ...
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0answers
56 views
Derive variance of the least squares estimator for $\beta$ [closed]
I want to prove the least squares estimator. Here is my proof:
$\beta = X'(X'X)^{-1} y$
$$Var((\hat \beta - E(\beta)(\hat \beta - E(\beta))'=E(\hat \beta - \beta)(\hat \beta - \beta)'$$
$(\hat ...
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1answer
62 views
How to prove that Manova is a special case of mixed models?
I am writing my master's thesis in quantile multilevel regression.
My professor all of a sudden decided to change the subject of my thesis into something that could be called "quantile multilevel ...
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1answer
62 views
Does $y'y= \hat y' y + e'e$ hold for the least square model?
I want to show that $y'y= \hat y' \hat y + e'e$ hold for the least square model. I found out that:
$\hat y= X b$ with $b$ the least squares estimator of the coefficient vector and $e$ the residual ...
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0answers
58 views
Proof for two-sample Hotelling $T^2$ statistic?
I've been reading "A primer of multivariate statistics" by Richard J. Harris, page 546, which shows how to derive the Hotelling $T^2$ statistic, after seeing this related but different question (I ...
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0answers
46 views
Proof that a and b in linear regression are random variables
I had posted this question http://math.stackexchange.com/questions/353703/proof-that-a-and-b-in-linear-regression-are-random-variables in math.stackexchange.com but I am certain that the reason why I ...
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0answers
41 views
About sigma algebra (proof of Borel field)
Suppose that the sample space S of some experiment is finite.
Show that the collection of all subsets of S satisfies the three conditions required to be called the collection of events:
$S \in ...
1
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1answer
48 views
Proof of distribution $\chi_n ^2$?
I have the problem of proofing that
$$X=(1/\sigma^2) \sum_{i=1}^{n} Y_i ^2$$
where $Y_i \sim N(0,\sigma^2)$ is $\chi_n ^2$ distributed with $E(X)=n$:
My proof that $E(X)=n$:
$$E(X)=E((1/\sigma^2) ...
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0answers
19 views
Euclidean distance prove [duplicate]
I know that Euclidean distance is a measure that may be used to compute the similarity between two vectors. Given a query q and documents d 1, …, dn, we may rank the documents d 1, …, dn in the ...
1
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1answer
41 views
Has Granger causality been used successfully in a industrial liability case?
Wikipedia claims that Granger causality is somewhat accepted as a way to prove event A caused event B. Has it ever been used to prove, for example, a company was responsible for industrial accident ...
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0answers
131 views
Total area under any probability density function
What's the name of the theorem that tells us that the total area under any probability density function, discrete or continuous, equals 1?
My stats book actually defines a PDF by requiring that
...
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2answers
110 views
Correlation of handedness to sexual orientation?
There have been studies done that report that heterosexual individuals are somewhat more likely to be right-handed than homosexual individuals. Does it necessarily follow that left-handed individuals ...
2
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0answers
45 views
Constant signs of correlation in the active set in least angle regression
I am trying to comprehend the proof of the Least Angle Regression algorithm and I am stuck at certain points. I would appreciate any help that I can get.
Let me set the stage:
I am following the ...
1
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3answers
86 views
How to prove that averaging averages of different partitions of a dataset produces the same overall average
After testing some cases, it appears to be true that if you create partitions in a dataset, average the data in the partitions, then average the averages, you get the same result as if you averaged ...
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0answers
50 views
Easy backgammon proof [closed]
Hopefully someone can offer a formal answer to this simple scenario, and end an argument between my wife and I:
If a game of backgammon is concluded, and throughout the game 1) neither player was ...
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1answer
138 views
Simple regression proof using general formula
I want to derive the least square estimation of the coefficients for $y=\beta_0+\beta_1*x_1+\varepsilon$ using the general formula.
Can someone walk me through how to get from B to D in the image ...
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2answers
441 views
A proof involving properties of moment generating functions
Wackerly et al's text states this theorem "Let $m_x(t)$ and $m_y(t)$ denote the moment-generating functions of random variables X and Y, respectively. If both moment-generating functions exist and ...
3
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1answer
92 views
Distribution of a centered standardized sample
Foreword : this is not homework, but a real problem : in a Bayesian model comparison context, I am trying to work out the correct prior density of mixed-model parameters which are, for computational ...
3
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0answers
77 views
Proving the convergence of KDE algorithms when the samples are non-i.i.d
I am currently working on convergence proof for a new method for non-parametric importance sampling, and I need some help...
My method uses an MCMC algorithm to generate a set of dependent $M$ ...
4
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1answer
181 views
Proofs of the central limit theroem
I know there are different versions of the central limit theorem and consequently there are different proofs of it. The one I am most familiar with is in the context of a sequence of identically ...
3
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1answer
117 views
Proof without Jensen
In the middle of an argument that I will present to my students I'll have to prove that $E[X^2]\geq E^2[X]$, but I don't want to use Jensen's inequality to do so. Is there any elementary way to go?
...
2
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1answer
1k views
Proof of how the normal distribution arises as the limit of the binomial — where do $\pi$ and $e$ come from?
I've always thought the emergence of the normal distribution was kind of magic, specifically that $\pi$ and $e$ both emerge in the distribution, even though they don't exist in the binomial.
I've ...
2
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1answer
227 views
Deriving OLS estimates using method of moments
I've worked the slope all the way down to $\sum [x_i(y_i - \bar{y})] = \hat\beta_1 \sum[x_i(x_i - \bar{x})]$
But I can not figure out how to show the steps for:
$\sum[x_i(y_i - \bar{y})] = \sum(x_i ...
-1
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1answer
201 views
proof FGLS asymptotically efficient
Prove that FGLS is asymptotically efficient. Does one have to use Cramer Rao to do this?
1
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1answer
157 views
Asymptotic Efficiency of Two-Stage Least Squares
Apparently Wooldridge, Introductory Econometrics, 2002ed is the only book showing that two-stage least squares (2SLS) is asymptotically efficient. I cannot get a copy of the proof.
Is it correct to ...
0
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0answers
498 views
Proof that sum of residuals and sum of $\hat{Y}$ residuals is 0
Can someone give me a hint on how to do this. All I was given is the MLR model
$$Y=BX+E$$
(all of them are vectors) and the hat matrix $H$ lemma.
2
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1answer
227 views
What happens with the beta-binomial distribution, when n approaches infinity?
Short question: What happens to the beta-binomial distribution, when n increases to infinity? Is there a count distribution arising like it's for the classical binomial distribution?
0
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2answers
352 views
Dispersionparameter of negbin distribution
Can anybody show me, why the Dispersionparameter of the negbin distribution is taken to be one? In the Poisson case you can show that E(y)/var(y)=$\mu/$\mu=1 which is called Equidispersion. But how ...
3
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1answer
314 views
Dual problem for L2 support vector machine
Here is the dual problem for L2 support vector machine:
$$\max_{\alpha\in\mathbb{R}^{n}} 2\alpha^{T}y-\alpha^{T}\left(K+n\lambda Id_{\mathbb{R}^{n}}\right)\alpha$$
$$\forall i\in\left\{ ...
15
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7answers
2k views
Is it possible to prove a null hypothesis?
As the question states - Is it possible to prove the null hypothesis? From my (limited) understanding of hypothesis, the answer is no but I can't come up with a rigorous explanation for it. Does the ...
2
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1answer
902 views
Regression Proof that the point of averages (x,y) lies on the estimated regression line
How do you show that the point of averages (x,y) lies on the estimated regression line?
3
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1answer
115 views
Large deviations proof question
Below is part of the proof of large deviations result. K is cumulant generating function. Can anyone explain how the last step follows?
This is page 157 of McCullagh's "Tensor Methods in ...
15
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1answer
2k views
Empirical Relationship Between Mean, Median and Mode
For a unimodal distribution which is moderately skewed, we have the following empirical relationship between mean, mode and median:
(Mean-Mode) ~ 3(Mean-Median)
Could someone please explain how the ...
7
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0answers
419 views
Testing (and proving) the randomness of numbers [duplicate]
Possible Duplicate:
Testing random variate generation algorithms
What's a good way to test a series of numbers to see if they're random (or at least psuedo-random)? Is there a good ...
