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### SVD of correlated matrix should be additive but doesn't appear to be

I'm just trying to replicate a claim made in the following paper, Finding Correlated Biclusters from Gene Expression Data, which is: Proposition 4. If $X_{IJ}=R_{I}C^{T}_{J}$. then we have: ...
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### Can the Mantel test be extended to asymmetric matrices?

The Mantel test is usually applied to symmetric distance/difference matrices. As far as I understand, an assumption of the test is that the measure used to define differences must be at least a ...
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### Gaussian Ratio Distribution: Derivatives wrt underlying $\mu$'s and $\sigma^2$s

I'm working with two independent normal distributions $X$ and $Y$, with means $\mu_x$ and $\mu_y$ and variances $\sigma^2_x$ and $\sigma^2_y$. I'm interested in the distribution of their ratio ...
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### Degrees of freedom of $\chi^2$ in Hosmer-Lemeshow test

The test statistic for the Hosmer-Lemeshow test for goodness of fit of a logistic regression model is defined as follows: the sample is split into $d=10$ deciles, $D_1, D_2, \dots , D_{d}$, per ...
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### In statistical learning theory, isn't there a problem of overfitting on a test set?

Let's consider the problem about classifying the MNIST dataset. According to Yann LeCun's MNIST Webpage, 'Ciresan et al.' got 0.23% error rate on MNIST test set using Convolutional Neural Network. ...
An univariate autoregressive process AR(p) process is expressed as $$y(n) = \sum_{j=1}^p a_jy(n-j) + u(n)$$ is excited by Gaussian sequence, $u$. Paper : On the Computation of the Cramer-Rao Bound ...