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]).
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Instrumental variable as a control variable
I understand that instrumental variable is used to address endogeneity bias since there could be correlation between the variable of interest and the error term.
Suppose now we want to see the ...
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Multiplicative BIASES in Log-Log regression
When we try to estimate elasticities by regression, we usually estimate the following regression model:
$$ln(y) = \beta_0 + \beta_1 ln(x_1) + \dots + \epsilon$$
When we expect to have endogenous ...
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How does non-collapsibility and the lack of an error term affect coefficients in regression
I have read from here that in nonlinear models such as the logit and Cox, because of a lack of an error term, coefficients may be biased (typically towards zero) when covariates are omitted; I see how ...
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What does it mean that BLUP is unbiased, given a linear two-level model?
Suppose we have the following mixed effects model for observation $Y_{ij}$ of pupil $i$ in school $j$:
$Y_{ij}=b_0 + u_j + e_{ij}$
Here, $b_0$ is a fixed parameter for the "grand mean", $u_j$...
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Bias vs consistency in instrumental variable estimation
So in Mostly Harmless Econometrics, page 154, they analyse the bias of instrumental variables:
They consider the case of one endogenous variable $x$, multiple instruments $Z$, and $\eta$ is the ...
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Treating longitudinal data as a repeated cross section
Can you introduce bias by treating longitudinal data as a repeated cross section?
Suppose I have two data sources measuring the same variables. The first is a balanced panel dataset $\{y^{long}_{it},X^...
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Why does the jackknife reduce bias? [duplicate]
Given a sample $x = (x_1, \ldots, x_n)$, define $x_{(-i)}$ as the sample values excluding sample $x_i$. That is,
$$
x_{(-i)} = (x_1, \ldots, x_{i-1}, x_{i+1}, \ldots x_n).
$$
Now given estimator $T(x)$...
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Why the MSE of the fitted data is not equal to the sum of the bias and the variance in R?
I use simple linear regression and I want to find the decomposition of MSE, that is as a sum of the bias, the variance and the variance of the error terms. I have the following code:
...
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Using Forecasted Data to Augment Predictions
We have a model that is predicting 5 year rent growth. We know that supply for the next two years is at a record high. We know that this record high supply is going to impact the rent growth ...
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Resample from a sample to match a desired distribution
Suppose I have observations $x_1,\dots,x_n$, sampled iid from some distribution on $\mathbb{R}$, with pdf $p(x)$. Suppose I wish I had a sample from the distribution with pdf $q(x)$. Is there a way ...
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For a biased estimator, how does one call the point for which the expected value of the estimator is equal to the observed sample estimate? [closed]
Let $\hat{\theta}$ be a biased estimator whose bias depends on the true value $\theta_0$, such that $E[\hat\theta|\theta_0]= f(\theta_0)\neq \theta_0$. Let $t_{sample}$ be a sample realization of $\...
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Expectile loss to reduce dependent variables overestimation
Say I have a a bunch of covariates $X$, and a dependent variable $y$, where $y$ is collected from people. However, I know from psychology that people will tend to overestimate $y$ given $X$ in some ...
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Is this a correct explanation of the asymptotic bias of maximum likelihood?
I want to be sure I understand, so please critique the following:
In regular parametric statistical models, the non-linear maximum likelihood estimator is biased. Given some data, $y_i$, parameters, $...
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Data taken from survey where survey-takers self report a continous variable
I have a problem with some health data that I'm trying to analyze. The main issue originates from a census variable is derived from self reported times. The variable is sleep duration, which is ...
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Why is the asymptotic bias of the maximum likelihood estimate $b(\theta) = \frac{b_1(\theta)}{n}+\frac{b_2(\theta)}{n^2}+...$?
Firth (1993) states in his introduction that for a $p$-dimensional parameter $\theta$ the asymptotic bias of the maximum likelihood estimate $\hat{\theta}$ may be written as:
$b(\theta) = \frac{b_1(\...
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