Questions tagged [bias]
The difference between the expected value of a parameter estimator & the true value of the parameter. Do NOT use this tag to refer to the [bias-term] / [bias-node] (ie the [intercept]).
1,120 questions
1 vote
0 answers
12 views
Asymptotic bias when misspecifying ARMA-X type model
Consider the following model: $$y_t = c_0 + \phi y_{t-1} + \beta x_{t} + u_t,$$ where $u_t$ follows an MA(1) process: $u_t = \varepsilon_t + \theta\varepsilon_{t-1},$ where $\varepsilon_t$ is white ...
- 11
5 votes
1 answer
233 views
Bias when estimating the best linear fit of a non-linear population?
If population data is non-linear (e.g. there is a clear strong exponential relationship), there is still a linear function that can approximate the relationship. I.e. there is a $y = α + βx$ that is ...
- 469
1 vote
0 answers
69 views
Order sensitivity of scoring rules
This is from another question here. The theorem below is from Lambert's paper about forecasting, (Elicitation and Evaluation of Statistical Forecasts): $\textbf{Proposition}\quad 1:$ Let $(\Theta = \{\...
- 111
1 vote
0 answers
44 views
input oriented Bootstrapping data envelopment analysis bias correction efficiency greater than one
In the input-oriented DEA model, efficiency scores typically range between 0 and 1. However, when using bootstrapping and bias correction for the estimator, some units have efficiency scores that ...
- 11
0 votes
0 answers
58 views
Binary Multi-armed bandit with unbounded time varying choice independent noise
I have $k = |K|$ arms with unknown distribution $\nu_\alpha$ over $[0,1]$ and unknown mean $\mu_\alpha \in [0,1]$ where $\alpha \in K$. The action $A_t \in \{1, \dots, K\}$ is chosen at time $t$ ...
- 101
2 votes
0 answers
55 views
Estimator bias implies Gradient Bias
Say I have a biased estimator, for example estimating $\log \mathbb{E}[f_\theta(x)]$ using Monte Carlo Does this implies that $\nabla_\theta \log \mathbb{E}[f_\theta(x)]$ is also biased if estimated ...
- 1,561
3 votes
1 answer
203 views
Bias of James-Stein Estimator
Suppose $X \sim N([\mu_1\space\, \mu_2\space\, \mu_3]^\intercal,I_{3\times3})$. The (sample size $n = 1$) James-Stein estimator of $[\mu_1\space\, \mu_2\space\, \mu_3]^\intercal$ is $$\hat{\mu}_{JS} = ...
1 vote
0 answers
53 views
Is there an one to one relationship between high bias and underfitting, and with high variance and overfitting?
Assume you have training data $(x_1,y_1), \ldots, (x_n,y_n)$ and a relationship $y_i=f(x_i)+\epsilon_i$, where $\epsilon$ is a random variable. Assume you approximate $f$ with $\hat{f}$ using the ...
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