Bias, in a statistical framework, means that an estimate of a parameter has an expected value that is not equal to the actual parameter value. There is often a tradeoff between bias and variance - low variance estimators may be more biased than high variance ones.
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5answers
770 views
Why is bias affected when a clinical trial is terminated at an early stage?
An interim analysis is an analysis of the data at one or more time points prior the official close of the study with the intention of, e.g., possibly terminating the study early.
According to ...
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votes
2answers
502 views
Is there a graphical representation of bias-variance tradeoff in linear regression?
I am suffering from a blackout. I was presented the following picture to showcase the bias-variance tradeoff in the context of linear regression:
I can see that none of the two models is a good fit ...
8
votes
3answers
327 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 ...
8
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3answers
251 views
OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equation?
Suppose ${X_{it}},{Y_{it}}$ are time series with $X_{it}\sim N(0.1,1)$, ($\sigma^2(Y_{it}) = 1$ and $mean(Y_{it})$ is similar to that for $X_{it}$, but changes when the dummy = 1). and $t \in ...
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votes
2answers
1k views
Overmatching bias and confounding variables
As I understand it, matching is one way to identify causality in observational studies. By matching observations that are "similar" and comparing ones that did or did not receive treatment, you can ...
6
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2answers
858 views
Bias - an intuitive definition
I'm struggling to grasp the concept of bias in the context of linear regression analysis.
What is the mathematical definition of bias?
What exactly is biased and why/how?
Illustrative example?
6
votes
1answer
83 views
How concerned should I be about the appropriateness of my prior?
As I understand it, selecting a prior provides something of a starting point for your analysis. From there, the distribution is shaped by the observed data. Obviously, the more data you observe, the ...
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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 ...
5
votes
4answers
3k views
Difference among bias, systematic bias, and systematic error?
Is there any difference among the following terms or they are same?
Bias
Systematic bias
Systematic errors
If there exist some differences then, please explain them. Can these errors be reduced ...
5
votes
1answer
207 views
Does Pearson correlation require removal of bivariate or univariate outliers?
Does the Pearson's correlation estimator require no bivariate outliers, or no outliers in each of two individual vectors of data? The answer will impact on how I winsorize outliers before calculating ...
5
votes
1answer
351 views
Omitted variable bias in linear regression
I have a philosophical question regarding omitted variable bias.
We have the typical regression model (population model)
$$
Y= \beta_0 + \beta_1X_1 + ... + \beta_nX_n + \upsilon,
$$
where the ...
5
votes
2answers
88 views
Training models on data that may be incorrectly classified?
I am working with some data that has been classified by domain experts. However, the classification they use is not 100% accurate. How can I deal with data that may not be correctly classified?
Are ...
5
votes
1answer
218 views
Biased estimates when intercept is included in a linear regression
I am simulating 10000 data-sets, each of length 20, that follow an autoregressive model with lag 1, using the following code:
...
5
votes
2answers
374 views
Cox proportional hazard model and non-randomly selected sample
Are there any methods to correct bias in Cox proportional hazard model caused by non-randomly selected sample (something like Heckman's correction)?
Background:
Lets say the situation looks as ...
4
votes
1answer
69 views
Literature on this kind of bias
Suppose I'm trying to investigate the lifespan distribution of light bulbs. The catch is that I can only observe each bulb at most $T$ time units. So if the bulb doesn't blow before $T$ I will not ...
4
votes
4answers
229 views
Assessing rater bias where one rater has given one very high rating and the remainder very low ratings
What is a good statistical test to check if there is a bias in judging in a situation that there is one judge that gave extreme scores (high score for one of the contestant and very low scores on the ...
4
votes
1answer
152 views
Bias of variance/precision estimator using Gamma prior
Assume I have $N$ samples $x_1, \cdots, x_N$ from a Gaussian random variable $X\sim N(\mu, \sigma^2)$ where both $\mu$ and $\lambda = 1/\sigma^2$ are unknown.
If I apply MLE, I have $\mu_{MLE} = ...
4
votes
1answer
139 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 ...
4
votes
1answer
172 views
Comparing structural equation models with multivariate non-normality
I am aware that multivariate non-normality in SEM can inflate the chi-square statistic and deflate standard errors of parameter estimates. I can deal with the latter (in AMOS) using bootstrapping ...
4
votes
0answers
220 views
Expected value of the natural log of a ratio of variances [closed]
I am dealing with a one-way random effects model and am looking for the $E(\ln(\hat{\sigma}_\alpha^2/\hat{\sigma}^2))$ where $\hat{\sigma}_\alpha^2$ is the estimate of the between group variance and ...
3
votes
1answer
159 views
Multicollinearity in OLS
I am reading Greene's textbook Econometric Analysis where he says that, if there's multicollinearity, then:
Small changes in data lead to large swings in parameter estimates.
Coefficients have high ...
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
90 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 ...
3
votes
2answers
284 views
Can a coin be biased?
If I have a coin that is not necessarily expected to turn up heads half of the time, then is it correct to call the coin biased? Or does bias in statistics only mean the bias of an estimator in which ...
3
votes
1answer
348 views
Correcting sample bias
I am studying the correlation of two observed variables (call them $A$ and $B$). the underlying distribution for $A$ is symmetric around $0$ (for sure), however in my sample I have $411$ observations ...
3
votes
1answer
123 views
Bias in classifier model selection
Say I have a set of classifier models, each generated using feature selection inside a repeated k-fold cross-validation. Each classifier model is generated using a different set of regularization ...
3
votes
2answers
85 views
How do you assess for mode bias and scale effects when designing survey questionnaires? [closed]
We typically educate clients on the potential bias of one mode over another (online versus paper surveys for example) and the bias a scale can have when designing questionnaires. A client recently ...
3
votes
1answer
252 views
What do the bias units represent in a restricted boltzmann machine?
I'm reading up on RBMs and this is not obvious to me. I'm imagining RBMs being used for something like the Netflix Prize (since that was one of the papers I read on it). So you have a bunch of ...
3
votes
2answers
134 views
Bias in sampling for set intersections
Say I have 2 sets, $A$ and $B$ with $n_{A}$ and $n_{B}$ elements respectively, which I assume is known. I would like to estimate $| A \bigcup B |$ using samples of $\tilde{A} \subset A$ and $ ...
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 ...
3
votes
1answer
100 views
When to use B'' or B''D as a measure of response bias?
I hope this is not a stupid question, but here it goes:
Based on information from Macmillan and Creelman's Detection Theory (2005) and Pallier's R-code that I found here, Computing discriminability ...
2
votes
4answers
243 views
Why must one trade off between bias and variance?
Apparently, a learning algorithm must make a trade off between bias and variance when producing a hypothesis. Bias means systematic deviation from data. Variance refers to the error due to ...
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votes
2answers
4k views
Conceptual understanding of root mean squared error and mean bias deviation
I would like to gain a conceptual understanding of Root Mean Squared Error (RMSE) and Mean Bias Deviation (MBD). Having calculated these measures for my own comparisons of data, I've often been ...
2
votes
2answers
135 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 ...
2
votes
1answer
65 views
Remove data starting before defined start date for survival analysis
I want to do survival analysis with a big data set.
The data collection started on 1997-01-01 and is still continuing yet.
However, episodes that started before ...
2
votes
2answers
98 views
How to assess whether experimental measurements obtained from different technicians are biased?
Suppose I have a list of measurements from an experiment; for example,
34 31 55 18 19 22 44 48 23 . . .
But I then learn that these experiments were conducted by two different technicians, so I ...
2
votes
1answer
68 views
Factoring in self selection bias
I am hoping to use some self selection survey data (it's from those awful things that pop up on the start page of a website asking if you have 5 minutes to spare).
This is for business decision ...
2
votes
1answer
80 views
Confusion related to the bagging technique
I am having a bit of confusion. I was reading this paper where it explained that bagging technique greatly reduces variance and only slightly increases bias. I didn't get it how come it reduces ...
2
votes
1answer
157 views
Using linear regression for bias correction
I have a predictor and the ground truth. I have found that I can use linear regression for bias correction, so instead of using the predictor's estimate directly, we can use the one obtained from the ...
2
votes
2answers
170 views
Removing human evaluator bias
I am working on machine translation evaluation, and am looking at ratings given by humans who are judging the quality of sentences produced by machine translation systems. The evaluators give fluency ...
2
votes
1answer
55 views
Re-estimate classification model with biased data
Let's say that I score (with, for example, a logit model) a group of 10,000 customers according to their potential of buying a product, and that I decide to contact the top 1,000 with a special offer. ...
2
votes
1answer
33 views
Detect bias in subset of Bernoulli processes
I'm looking for advice on the best method to use to answer this question.
General scenario:
We have multiple testing machines A,B,C,D etc. each tests a identical randomly selected part and provides ...
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 ...
2
votes
0answers
43 views
The bias of Zellner estimators in dynamic SUR models
I have been playing around with a seemingly unrelated regression (SUR) estimation. However, for dynamic SUR models it is known that -- analogous to the ARIMA case -- an OLS/GLS estimate is biased. For ...
2
votes
0answers
69 views
Is it OK to use the CLT to create a normal distribution where there is none?
I have some data that looks like this:
Procrastinator has come up with one good suggestion for how to test hypotheses under this distribution, but it relies on some guesswork to fit constants. I ...
2
votes
0answers
89 views
Generalized Linear Models and Curse of Dimensionality
I was wondering what happens to bias and variance of GLM estimates as dimensionality approaches the number of training data points? Specifically in Linear Regression and Poisson Regression?
I know ...
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vote
1answer
58 views
What is bias in aerosol data?
I was reading this information related to aerosol, especially aerosol optical depth of the MISR and MODIS instruments. I didn't actually get what bias means in the context of the AOT retrievals of ...
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vote
2answers
237 views
Omitted variable bias in time series
This is a brief question because my lecturer mentioned it today in class but I don't quite understand. Why is omitted variable bias not a major problem in time series analysis?
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vote
1answer
555 views
What is bias correction?
I have seen many places where they have input/output datasets where they first create a linear regression line, correct the bias, and then only use that data for their model. I didn't get what this ...
1
vote
1answer
199 views
Time-Series Data and Omitted Variable Bias
I understand that ,usually, time-series studies do not aim to provide a causal explanation of anything but rather aim to forecast. In which case it does make sense that most time series studies aren't ...
