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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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### 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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### Fisher information in a hierarchical model

Given the following hierarchical model, $$X \sim {\mathcal N}(\mu,1),$$ and, $$\mu \sim {\rm Laplace}(0, c)$$ where $\mathcal{N}(\cdot,\cdot)$ is a normal distribution. Is there a way to get an ...
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### Is there a result that provides the bootstrap is valid if and only if the statistic is smooth?

Throughout we assume our statistic $\theta(\cdot)$ is a function of some data $X_1, \ldots X_n$ which is drawn from the distribution function $F$; the empirical distribution function of our sample is ...
### Degrees of freedom of $\chi^2$ in Hosmer-Lemeshow test
The test statistic for the Hosmer-Lemeshow test (HLT) for goodness of fit of a logistic regression model is defined as follows: the sample is split into $d=10$ deciles, $D_1, D_2, \dots , D_{d}$, ...