3
votes
1answer
46 views

Estimates of regression coefficients are uncorrelated?

Consider a simple regression (normality not assumed): $Y_i = a + b X_i + e_i$ where $e_i$ is with mean 0 and standard deviation $\sigma$. Are the Least Square Estimates of $a$ and $b$ uncorrelated?
1
vote
0answers
27 views

Help in Maximum likelihood etimation in presence of colored noise

I am trying to test system identification in presence of measurement noise (1) A white Gaussian noise (2) Colored noise - pink, violet. When we are estimating parameters we do so in presence of iid, ...
3
votes
2answers
60 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
38 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
247 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
445 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 $\ ...
5
votes
1answer
186 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
385 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
1k 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 ...
15
votes
3answers
944 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 ...