Tagged Questions

3
votes
1answer
92 views

What is an unbiased estimate of population R-square?

I am interested in getting an unbiased estimate of $R^2$ in a multiple linear regression. On reflection, I can think of two different values that an unbiased estimate of $R^2$ might be trying to ...
2
votes
0answers
49 views

Estimator bias without a closed form?

Given a regression loss function $l(Z,\beta)=||Y-Z\beta||_2 + \lambda \beta^TD\beta + r(X,Z)$ where $X$ is the predictor matrix, I would like to estimate a $Z$ that minimizes the above loss in a ...
8
votes
3answers
332 views

Parameter estimation of exponential distribution with biased sampling

I want to calculate the parameter $\lambda$ of the exponential distribution $e^{-\lambda x}$ from a sample population taken out of this distribution under biased conditions. As far as I know, for a ...
3
votes
1answer
328 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
77 views

Correcting biased polling

Let's say I'm polling for a binary election in different states with known biases. Furthermore, let's say I only manage to poll only a small sample of people in each of these states. How would you ...
4
votes
1answer
140 views

What is the estimation bias of the top estimate in a list sorted by value?

Let's make the problem as simple as possible. Assume two related random variables, $X_1$ and $X_2$. On the basis of some data we estimate their true means $\mu_{X_1}$ and $\mu_{X_2}$ by sample means ...
2
votes
2answers
136 views

Can the ratio importance sampling estimate by made to be unbiased with resampling?

Consider approximating the following integral: $$ \mathcal{Z} = \int h(x) \pi(x) dx $$ Where $\pi$ is known only up to a normalizing constant, that is, $\pi(x) = \hat{\pi}(x)/\mathcal{Z}_\pi$. We can ...
5
votes
4answers
2k views

Why is it claimed that a sample is often more accurate than a census?

When learning the course of sampling, I meet the following two statements: 1) Sampling error leads to mostly variability, nonsampling errors lead to bias. 2) Because of nonsampling error, a sample ...