How to decide the most possible signal model between two model candidates besed on the received signal vector? Assume the received signal vector is $y$, the possible signal model …

I would like to understand the relation (if any) between the Cramer-Rao Lower Bound of estimation theory and the following simple definition of "reconstruction accuracy" which does …

I've been using iteratively reweighted least squares (IRLS) to minimize functions of the following form, $J(m) = \sum_{i=1}^{N} \rho \left(\left| x_i - m \right|\right)$ where $N …

Today I came a cross an old math thing I did some years ago. I remembered that I didn't find a similar result from anywhere at that time but forgot the thing altogether. So now I w …

Sorry for the vague title but I couldn't find a better one. I want to compute the sum $S = \frac{1}{N}\sum_{i=1}^N c_i x_i$ where $c_i$s are known positive constants. The problem …

I trying to find a reference on the optimal rate of convergence in Sobolev space. Given a regression model on interval $[0,1]$ $$ Y_{i}=f(x_{i})+\epsilon_{i},\ i=1,\ldots,N $$ wit …

I am in the early stages of a problem that involves parsing a large number ($\approx 5 \times 10^9$) of documents (web pages) and estimating values from them. In particular I need …

I have a signal and i'd like to estimate its temporal correlation. My limited understanding is i should compute the PSD by estimation using a parametric model such as AR. However …

Vectors y1 and y2 are estimators of y, both of which are unbiased. Is there any criteria to decide which one is better? There isn't any measured values for y1, y2 and y so I can't …

Given an unbiased estimator $\hat \theta_n$ of a parameter $\theta$, if the estimator has small variance (approaching $0$ as $n\to\infty$), it seems reasonable to expect that the e …

I have a bag with some marbles inside and we know (or are limiting our consideration to the possibility) that only red, green, and blue marbles exist. I sampled a few times (each w …

Hi, for fitting empirical data to power-law I am aware of the work by Clauset et al. (http://arxiv.org/abs/0706.1062) and how to use maximum likelihood estimation. There exists a …

Hello, Assume I have random variables $X$ and $Y$. $X$ is observable; $Y$ is not. We also know that, if $X \leq Y$, $Z = f(X,Y)$ where $Z$ is a third random variable and $f(\cdot) …

I was reading through some notes deriving the different variances for confidence and prediction in OLS. Before dwelving into it though, the notes say that the standard error of $b_ …

Given $\textbf{x}=[x_1 x_2 ... x_n]^T$ where $\textbf{x} \in \{ 0, a_1, a_2, a_3\}^n, a_i \in \mathbb{C}$ and $\textbf{z} = \{z_1 z_2,...,z_n \}$ where $z_i \textbf{~} N(0,\sigma^ …