All Questions
Tagged with bias unbiased-estimator
86
questions
1
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0
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45
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Question on nonlinear least squares
Consider the following equation for $Y>0$:
$$
(1) \quad \log(Y)=\log(\gamma)+\log(\alpha+\beta X)+\epsilon.
$$
Assume that $E(\epsilon| X)=c\neq 0$. What are the consequences of this assumption on ...
- 889
1
vote
0
answers
58
views
Degrees of freedom for biased sample autocorrelation function
I want to find the expression for the a biased estimate of the autocorrelation function for a time series $X$, and am doing this from the biased estimated autocovariance function for lag $k$, divided ...
- 704
7
votes
1
answer
69
views
On unbiasedness of an optimal forecast
Diebold "Forecasting in Economics, Business, Finance and Beyond" (v. 1 August 2017) section 10.1 lists absolute standards for point forecasts, with the first one being unbiasedness: Optimal ...
- 68.6k
1
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0
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52
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Proof of attenuation bias in multiple linear regression model
Consider the case of measurement error with a single explanatory variable measured with error
\begin{equation}
y=\beta_0 + \beta_1 x_1 + \beta_2 x_2 + ... + \beta_k x^{\ast}_k + \nu
\label{...
- 309
3
votes
1
answer
72
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Tossing Until First Heads Outcome, and Repeating, as a Method for Estimating Probability of Heads
Consider the problem of estimating the heads probability $p$ of a coin
by tossing it until the first heads outcome is observed. Say we get $k_1$
tosses, then $U_1 = \frac{1}{k_1}$ is an estimate for $...
- 33
0
votes
0
answers
62
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How can I compute the expected value and variance of the 4th power of the sample median?
Given the following parameter estimate, how do I find $E[\hat{a}_{MED}]$ and $Var[\hat{a}_{MED}]$?
\begin{equation}
\label{eq:Estimator_a_Med}
\hat{a}_{MED} = - \left( n_0 \right)^4 \cdot \log(0.5)...
2
votes
1
answer
177
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Does an endogenous variable bias the coefficient of the exogenous one?
We have the following model:
$$ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \epsilon. $$
We know that:
\begin{align*}
\operatorname{Cov}(x_1, \epsilon) &\neq 0 \\
\operatorname{Cov}(x_2, \epsilon) &...
- 2,301
2
votes
0
answers
92
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Expectation of Difference in Means estimator
Given i.i.d. observations $(Y_i, X_i)$ where $Y_i$ is the response and $X_i$ is binary valued, the difference in means estimator is
$$
\hat{\theta} = \frac{1}{n_0} \sum_{i=1, X_i=0} Y_i - \frac{1}{n_1}...
- 1,501
1
vote
1
answer
49
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Can you correct "bias" in a regression if you can measure/model it? A journey in missing data and reweighting test scores
Thank you for joining me on this semi-theoretical journey. Here we will discuss how to account for "predictable" bias in your data.
Let's say we have a test composed on many subtests. A ...
- 213
0
votes
1
answer
106
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Property of unbiased estimators
If $f(x)$ and $f(y)$ are both unbiased estimators of $\mu$, aka $E[f(x)]$ = $E[f(y)]$ = $\mu$, is it possible that $f((x+y)/2)$ is also an unbiased estimator of $\mu$?
We know $f((x+y)/2)$ would be ...
- 31
14
votes
5
answers
4k
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Does the biased estimator always have less variance than unbiased one?
Suppose I am estimating one of the parameter. Now if we plot the biased estimator of that and unbiased estimator of that can we say for sure that biased one has less variance than unbiased one always.
...
- 299
3
votes
1
answer
619
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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
2
votes
1
answer
135
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Bias-variance trade-off in case of biased estimators: is the bias zero?
Consider a data generating process (DGP) that is AR(1): $y_t=\varphi_1 y_{t-1}+\varepsilon_t$ with $\varepsilon_t\sim i.i.D(0,\sigma^2)$ for some distribution $D$ with mean zero and variance $\sigma^2$...
- 68.6k
1
vote
2
answers
1k
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Definition of the bias of an estimator
I'm quite confused about the definition of the bias of an estimator.
Suppose we have unknown distribution $P(x, \theta)$, and construct the
estimator $\hat{\theta}$ that maps the observed data sample ...
- 11
9
votes
3
answers
1k
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Asymptotic bias of LASSO vs. none of SCAD
I am reading a paper which says that LASSO is asymptotically biased while SCAD is not. I take asymptotic (un)biasedness to concern the slope estimators from LASSO and SCAD as the sample size goes to ...
- 68.6k