3
votes
2answers
53 views

Recovering true data from many noisy samples with varying unknown amounts of noise

Input: $k$ vectors $x^1,\ldots,x^k \in \mathbb{R}^n$, where $x^i \sim \mathcal{N}(x,\mathbb{1} \cdot \sigma_i^2)$. Goal: approximate the vector $x$ as well as possible. The quality of approximation ...
2
votes
1answer
36 views

inequality in bivariate normal variable

Let $U_1=(X_1,Y_1)^T,\dots,U=(X_n,Y_n)^T$ are i.i.d. copies of $U=(X,Y)^T\sim N_2(0,\Sigma)$ where $$ \Sigma= \begin{pmatrix} \sigma^2 & \rho\sigma\tau \\ \rho\sigma\tau & \tau^2 ...
1
vote
0answers
204 views

Discussion about proxy- and instrument variables and endogeneity in the context of a multi equation model

Assume two equations $Y_1 = X_1\beta_1 + X_2\beta_2 + U_1$ $Y_2 = X_1\alpha_1 + X_2\alpha_2 + U_2$ Further assume that $ \ U_1 = X_4 + E_1$ and $U_2 = X_4 + E_2$ with $ \ corr(Y_1,X_4)\ne 0, \ \ ...
3
votes
1answer
435 views

Looking for a OLS-Equation if one Regressor is correlated with the error

How can I express a OLS-Estimator if I know about the correlation i.e. I know that $E(x_i u_i)=\rho$ (I'm not looking for IV or 2SLS). I'll explain my problem with an example: In a simple problem $\ ...
3
votes
1answer
173 views

Joint distribution of two sums of correlated variables

Suppose that $(X_1, Y_1)$ and $(X_2, Y_2)$ are independent and have the same joint distribution $F_{X,Y}$, which is a known copula $C_{X,Y}(F(X), F(Y))$. Also, suppose that $V = X_1 + X_2$ and $W = ...
2
votes
0answers
364 views

Ties in the data

Are there any "good" ways to eliminate the effects of ties in a data set for statistical analysis? For example, in finding the correlation between two series which has lots of ties? I would like to ...
2
votes
0answers
38 views

Calculating/approximating complete Mantel statistic from bootstrap estimates

I have two (sparse) large matrices (~ 1million by 1million) and want to compute Mantel statistic to find correlation between them. To counter memory problems, I have computed the mantel statistic ...
0
votes
2answers
978 views

How to estimate correlation matrix from largest eigenvalues?

I'm trying to estimate a correlation matrix from the 5 largest eigenvalues and associated eigenvectors of the sample correlation matrix. My problem is that the output from the following Matlab code ...
14
votes
3answers
891 views

Unbiased estimation of covariance matrix for multiply censored data

Chemical analyses of environmental samples are often censored below at reporting limits or various detection/quantitation limits. The latter can vary, usually in proportion to the values of other ...