Search Results

A ``down-to-earth'' observation to see what goes wrong with method of moments is this: When considering applying the method of moment to $(X_1,...,X_n)$, you may as well apply the method of moments to …

It is true under the assumption $k,d\to+\infty$ while $k/d\to 0$, in the sense that $R^T\in R^{d\times k}$ has obviously iid $N(0,1)$ entries, and satisfies $$ \|\sqrt d R^+ - R^T/\sqrt d\|_{op} \to^ …

I believe the probability is at least $\approx0.343$. Let $\mu_n$ be a probability measure giving $q_n = P_n[ X_1 + X_2 + X_3 < 2X_4]$. Consider now $(Y_i)_{i\le 4}$ Bernoulli$(p)$. The $Y_i$'s produc …

For two measurable sets $A,B$, let $p=\mu(A)$ and $q=\nu(B)$. Consider any coupling of a Bernoulli$(p)$ and a Bernoulli$(q)$, say, $C:\{0,1\}^2 \to [0,1]$. Then we can find a coupling $(X,Y)$ of $\mu …

The paper Chao, C., Bai, Z., & Liang, W. (1993). Asymptotic Normality for Oscillation of Permutation. Probability in the Engineering and Informational Sciences, 7(2), 227-235. doi:10.1017/S0269964800 …

Write the SVD of $\Gamma$, say $\Gamma = \sum_i q_i s_i v_i^T$. with $s_1,...,s_n>0$ the singular values and $q_i, v_i$ are the left and right singular vectors. If $Q=[q_1|...|q_n]$, $B=diag(s_1,...,s …

Assume real entries. Let $b$ be a column of $A$ and write $\tilde A$ the matrix $A$ with that column removed so that $AA^T = \tilde A\tilde A^T + bb^T$. By the https://en.wikipedia.org/wiki/Sherman%E …

If $H$ has iid $N(0,1)$ entries, write $\kappa=\langle Z^TZ, H\rangle$ using the usual Frobenius inner product $\langle A,B\rangle = trace[A^TB]$. Conditionally on $Z$, $\kappa\sim N(0,\|Z^TZ\|_F^2)$ …