All Questions
Tagged with bias estimation
60
questions
0
votes
0
answers
9
views
How to deal with Bias Gradient Matrix for biased CRB(Cramér–Rao bound) calculation if the gradient matrix is m-by-n but $m \neq n$?
I am doing a model for collabrative localization and using the CRB(Cramér–Rao bound) as the localization performance measurement. I want to consider interference caused by NLOS and clutter, therefore ...
0
votes
1
answer
34
views
Expectation of reciprocal residual sum of squares
Consider an IID sample $X_1 , \cdots, X_n \in \mathbb{R}^d$, then what can we say about the expectation of the reciprocal residuals when projecting onto every other point? That is can we compute
$$
E \...
- 31
3
votes
1
answer
40
views
Can we get the conditional bias of the estimator at a generic $x$?
Consider a standard ERM problem based on quadratic loss where we solve
$$
\hat{f}_n\in \operatorname*{arg min}_{f\in \mathcal{F}} R_\text{tr}(f)
$$
where $R_\text{tr}(f)=\frac{1}{n}\sum_{i=1}^n (Y_i-f(...
- 173
4
votes
1
answer
188
views
Proving that the bias of the derivative of Parzen-Rosenblatt (kernel density) estimator is of order $O(h^2) $ and $O(h)$ when $h$ approaches $0$
I came across this property that I don't get and I couldn't find the proof anywhere:
Suppose we have a density $K$ of the standard normal distribution and $K'$ its derivative. Suppose that the density ...
- 241
7
votes
2
answers
449
views
How to prove unbiasedness/consistency/normality of an estimator that doesn't have a closed form?
My estimator looks like this:
$$
\hat\theta(X) = \arg\max_{\theta} \frac1N \sum_{n=1}^N f(x_n|\theta)
$$
Here, $f(x_n|\theta)$ is some arbitrary function: it's not a logarithm, and the sum is not a ...
- 330
3
votes
1
answer
619
views
What is an "unbiased forecast"?
Assume we estimate a model from the data $(X, Y)$, with some estimator $W(X, Y)$, which is estimating parameters $\theta$ for the model we chose.
Then, we would like to perform a forecast for $Y_h$ ...
- 1,154
1
vote
0
answers
50
views
Bias in estimation of a latent / hidden variable drawn from a skewed distribution: what is it called?
I observe a bias effect in my measurement system that I can explain and correct using a simple latent or hidden variable model. I am sure this kind of effect has been described earlier in other fields ...
- 11
1
vote
1
answer
7k
views
How to calculate the expected value of an estimator?
According to my book :
An estimator, say, T, of the parameter $ \theta $ is said to be an unbiased estimator of $\theta$ if $ E\left( T\right) = \theta$.
It then explains how to calculate $E\left( T\...
- 37
3
votes
1
answer
111
views
How can i find bias of estimator for specific value?
I have $X_1,...,X_n~ Ber(p)$ with MLE estimator $\hat p$ which is equal to sample mean. I need to find bias of estimator $\hat p(1 - \hat p)$ for $p(1-p)$.
I presume $p(1-p)$ is variance of my RVs, so ...
- 33
1
vote
1
answer
131
views
What is the distinction between bias in prediction and parameter estimation?
I am trying to understand the distinction between bias in prediction and parameter estimation. This example in Gelman, Bayesian Data Analysis, 2nd ed. 2004 pp. 255-256 is very confusing to me.
Why do ...
- 869
3
votes
1
answer
3k
views
Can bias of an estimate be decreased by increasing sample size?
I understand that in case of consistent estimates, larger the sample size, there's a higher probability that the estimate converges to true value of parameter. Now, using the sufficient condition of ...
- 1,387
2
votes
1
answer
356
views
VAR models vs univariate models
Suppose I know the true DGP is a VAR(1) process. Instead of fitting a VAR model, I can still fit univariate ARMA models to each of its components.
Does anyone know whether it will result in biased ...
- 681
2
votes
0
answers
105
views
Estimation and hypothesis testing for the difference in squared bias for two random variables
My Question:
Let $X_t$ and $Y_t$ denote two time-series random variables, both of which are estimates of the random variable $\theta_t$. Let $U_t = X_t - \theta_t$, and $V_t = Y_t - \theta_t$. The ...
- 817
0
votes
0
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13
views
How to interpret an estimation system that predicts individual measurement poorly but provides unbiased mean?
I am trying to develop an automatic system to use machine to measure or estimate the length of a certain species. The system output gives quite strange result (figure below): From a regression point ...
- 2,121
1
vote
1
answer
253
views
Show that bias term involving an indicator function convergences to zero
Assume that we have $N$ observations of i.i.d. data $(Y_i,X_i)_{i=1}^{N}$. We want to learn the model given by $Y=f(X)+\epsilon$. We use the data to estimate $\hat{f}$ using any machine learning ...
- 115