3 problems

Let $\hat{\theta}_n$ be the maximum likelihood estimator of the location parameter $\theta$ in the Pearson Type VII model, and let $m$ denote its shape parameter. Mean-squared-erro…

Let $n$ denote the sample size, let $MSE(\text{entropy estimator})$ denote the mean squared error of an entropy estimator, and let $b$ be the corresponding exponent. Conjecture. Fo…

Let $x\in\mathbb{R}^N$ be the signal, $y=\Phi x+z$ the measurement vector, and $x^U_{MAP}$ the universal MAP estimator. Assume that $\Phi\in\mathbb{R}^{M\times N}$ is an i.i.d. Gau…