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      Questions tagged [st.statistics]

      Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

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      41 views

      Overview of interpretations of classical probability

      The Stanford Encyclopedia of Philosophy has a nice overview of numerous different interpretations of probability (classical as opposed to quantum) with an extensive bibliography. What books would ...
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      0answers
      31 views

      Concentration or distribution of the scaled $l_p$ norm of a correlation matrix

      Background: Among Hermitan random matrices, correlation matrix has a lot of applications in statistics. People have studied the "empirical spectral distribution (ESD)" of a correlation matrix, the ...
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      29 views

      Low rank matrix recovery — generalization of spectral method to nonlinear noise model

      Suppose $X^{\star}$ is an $n \times n$ matrix with rank $r$, where $r \ll n$. We aim at recovering $X^{\star}$ from a noisy observation $Y$. People have throughly studied the noise model $Y_{ij} = X^...
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      13 views

      How to perform regression with different error variances? [migrated]

      I have two series of measurements values, first series is X and second is Y. I need to model Y as a function of X, where I know the method that was used to measure X is two times better then the ...
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      50 views

      Reference: Maximum Entropy Principle

      It seems that the derivations of the maximum entropy distributions is a "well-known" fact and so it is in the continuous and discrete cases.... However, I can't seem to find a proof/formal statement ...
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      1answer
      57 views

      Convexity of exponential family

      It is known that (given a $\sigma$-finite Borel reference measure $\nu$ on $\mathbb{R}$) the parameter space of an exponential family is convex in Euclidean space. However, my question is, for an the ...
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      votes
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      45 views

      On $\ell_1$ to $\ell_1$ operator norm of matrix with inverse Wishart distribution

      Consider a random $n\times p$ matrix $X$ with $n\ll p$ and all entries of $X$ i.i.d. standard normal. For this $X$, the system of linear equations $y=Xw$ has infinitely many solutions, and the one ...
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      46 views

      Information theoretic lower bounds for sparse recovery

      For the well-known problem of sparse recovery using $\ell_1$ minimization, it was shown in this paper that for any random measurement matrix, a recovery procedure that succeeds with constant ...
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      22 views

      Minimal representation of t(y)

      I have an extended F-distribution with density $$\frac{1}{B(0.5d,0.5d)}y^{d/2-1}(1+y)^{-d}$$ for $y \geq 0$ and $d>0$ and ${B(0.5d,0.5d)}$ is the beta function. I have in canonical form the ...
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      1answer
      160 views

      Bounding the sensitivity of a posterior mean to changes in a single data point

      There is a real-valued random variable $R$. Define a finite set of random variables ("data points") $$X_i = R + Z_i \; \text{for } i\in\{1,\ldots,n\},$$ where $Z_i$ are identically and independently ...
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      53 views

      Physical meaning of dividing the mean square by variance of a distribution

      In the field of chromatography, the so-called "efficiency" a Gaussian peak or at times an exponentially modified Gaussian peak is expressed as the mean squared divided by the variance of the peak. The ...
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      2answers
      168 views

      Find $\inf_{P_{X_1,X_2}}P_{X_1,X_2}(\|X_1-X_2\| > 2\alpha)$ , where $\alpha > 0$ and inf is over couplings

      Let $\mathcal X$ be a seperable Banach space with norm $\|\cdot\|$, and let $X_1$ and $X_2$ be random vectors on $\mathcal X$ with finite means. Question. Given $\alpha > 0$, what is value of, ...
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      1answer
      41 views

      Expectation of $\left| \frac{(\textbf{x}+\textbf{y})^{H} \textbf{x} }{\| \textbf{x} + \textbf{y} \|^2} \right|^2$, with complex Gaussians?

      Given that following two random variables $\textbf{x} \sim \mathcal{CN}(\textbf{0}_{M},\sigma_{x}^{2}\textbf{I}_{M})$ and $\textbf{y} \sim \mathcal{CN}(\textbf{0}_{M},\sigma_{y}^{2}\textbf{I}_{M})$ ...
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      65 views

      Concentration inequality for minimal eigenvalue of sample covariance

      I was reading an article of matrix completion and met the following lemma The concentration inequality for $\sigma_{\max}$ part is a standard result. However, I didn't find any results like the $\...
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      26 views

      Linear combination of constrained random variables, and its convergence

      I have positive random variables X1, X2, X3, ..., Xn such that their sum=1 (so they are random, subject to constraints that each Xi is positive their sum has to be 1.. so all are fractions). Now, I ...

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