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You could try a moment-matching approach. In particular, define $\hat{s}$ to be the value of $s$ such that $$\mbox{Pr}_{s}(-1 < r < 1) = \frac{\sum_i I(-1 < r_i < 1)}{N}$$ where $N$ is the number …

One key word would be "seemingly unrelated regressions" or SUR. The dependence of the noise term leads to different estimates of the regression coefficients (your $A$): http://en.wikipedia.org/wiki/S …

The distribution shown is not a Wishart distribution, it is a multivariate t-distribution. This is the marginal distribution of $X$ after integrating the covariance matrix out of the Gaussian sampling …

Others have hit on this, but I thought I'd contribute how I'd write the problem down (briefly): Let $x_i \sim N(m, 1)$ for $i \in \lbrace 1, \dots, N\rbrace$ and define $y_i \equiv x_i$ if $x_i > 0 …

I think there are two separate things going on here. One is the issue of a maximum entropy distribution. The other is of whether or not distributions are invariant under different parameterizations. …

The difference between PCA and FA can be thought of in terms of the underlying statistical models (regardless of estimation methods, although these will change depending on the model used). Consider …

There is a whole research area called Algebraic Statistics, although its boundaries are pretty blurry in my opinion. But you could do worse than to start with Seth Sullivant's web page for some idea …

If a student walks away understanding the distinction between an estimand, an estimator and an estimate, along with the idea of a sampling distribution, you will have done an above average job. Equipp …

If the $\mu_X(t)$ and $\mu_Y(t)$ are bounded for all values of $t$, we may try to construct a statistic that has a mean of $\mu_X(t)^2 - \mu_X(t)\mu_Y(t)$ for all $t$. Under the hypothesis, this mean …

Apparently it's something to do with the "residuals" function in R. If you do this h <- fitted.values(lm(tan(c/2)~u)) plot(u,h-tan(c/2),ylim=c(-2e-16,2e-16),cex=0.1) instead (with the previous co …

I think the difficulty is worse than just finding the right algorithm. The first matter of business is deciding which conditional distribution you want to draw from, because they are non-unique. I'm …

Total variation and Hellinger distance are two standard ways to measure this. Kullback-Leibler divergence is another standard way, as would be general $f$-divergences. The Earth-Mover's distance (al …

This is not an answer, but maybe worth thinking about (and I cannot yet leave comments). My intuition about the Stein phenomenon is that while the individual coordinates of the Gaussian random variab …

The ridge estimator corresponds to the posterior mean under a Normal linear regression model with a conjugate Normal-inverse-gamma prior on the regression coefficients: $\beta \mid \sigma^2, \lambda …

The result you want, I think, is in Stationarity, Isotropy and Sphericity in $l_p^*$. It is behind a pay-wall, but the form of the distribution is stated in the abstract.