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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How to deal with 'cut-off' selection bias/sampling bias? (truncated distribution)

In short When measuring an outcome with a normal distribution, but whos mean is below the detection threshold, can you still make statements about differences between populations? Example Say I ...
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extrapolation and selection bias

I have a cohort of patient data. I have 100 Affected and 900 UnAffected I am reassessing one of the variables for each of the patients, however I can only do so for 90 Affected and 200 UnAffected. ...
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The mystic “true” bias (bootstrap-method)

This is a problem of understanding. That's why it doesn't include any formula. I have one big data set (n=83 Observations) and a small subdataset (n=15). With the small subdataset, I estimated the ...
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86 views

Summary of estimator properties (consistency, bias, sufficiency, etc.)

I've read about various properties of estimators, but I'm wondering if there's some source with a summary (maybe a list, table, or graphic) of the properties for different kinds of estimators. ...
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9 views

Is regression dilution bias avoided by using time-dependent predictors?

Regression dilution bias implies that even random measurement errors may bias the results by pushing the regression slope towards zero. Cross-sectional studies are particularly susceptible to ...
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14 views

Skellam Distribution with Dummies (Difference of two Poisson RV)

The difference of two Poisson distributed random variables follows a Skellam distribution. We know that a Maximum Likelihood estimation using Poisson distribution yields consistent estimates also in ...
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16 views

Controls sampled on confounding variable

Let's say I wanted to use logistic regression to analyze the effect of an exposure variable on a categorical outcome variable ("yes" or "no"). I believe there are two important confounding variables ...
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13 views

Estimating population mean when using biased sampling?

Say you had a sample of 50 items that was constructed by taking selecting values that were in the top 75% (not in the first quartile), and you had to take 61 items to find those 50 (11 were in the ...
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How can increasing the dimension increase the variance without increasing the bias in kNN?

My question is about understanding Figure 2.8 in The Elements of Statistical Learning (2nd edition). The topic of the section is how increasing dimension influence the bias/variance. I can roughly ...
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67 views

If $\operatorname{Var}\left(\epsilon_i\right) = h\left(X\right) \neq \sigma^2$, what can we know about $\operatorname{Var}\left(\hat{\beta}\right)$?

This question uses the derivations found here. The short version Consider a regression model. If the error variance is a known function of the data (rather than a constant), under what conditions ...
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49 views

Omitted Variable Bias in Linear Regression - Simulation

Is the following a reasonable illustration of the OVB problem? We build up fictional data around the regression line: $$y = 7.2 + 2.3 \, x_1 + 0.1 \, x_2 + 1.5 \, x_3 + 0.013 \, x_4 + eps$$ by ...
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Publication bias in meta-analysis of single observation studies

I have conducted a systematic review and lme model of 50 studies attempting to economically value ecological services (previously un-valued). These studies do not use data samples or observations, ...
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Bias Correction for Large Scale Logistic Regression with Rare Events

I have a large dataset constituted of many ad impressions. My dependent binary variable clicked describe whether or not the ad was clicked on. As you can expect, the number of clicks is about 1000x ...
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2answers
115 views

How to draw a representative sample from a biased portion of a sampling frame?

I have a question concerning sampling. We are planning a study in which we aim to draw conclusions about the relationship between different sources of research funding and academic impact (measured ...
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1answer
24 views

Contribution of a sample to cross validation error

I was wondering how to asses which sample in the data, during K fold cross-validation drives the bias that may be observed in the results. My training data consists of 40 samples. And I try to ...
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26 views

Inferring the bias of two types of coin

I would like to find the bias of a type of coin, when there is uncertainty about which kind of coin I am testing. The scenario is as follows, there are 2 mints in my neighbourhood that produce ...
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1answer
27 views

What do you mean by pollster bias in an election?

I came across harvards election poll data science question. I which they ask: Is there a pollster bias in presidential election polls? What exactly is a pollster bias? can some one explain it to me in ...
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28 views

Individual-specific error component in pooled OLS

I know that Pooled OLS is not efficient if there is existence of the individual-specific error component (one that doesn't vary over time) because the usual standard errors are incorrect and the tests ...
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Modeling change over time when response variable has different range and variance?

Some background: I am working with data from a large cohort study. My outcome is a measure of fine motor skills, and was adapted from a psychometrically validated instrument (the short version ...
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45 views

bias and sampling

This was an interview question I encountered. can some one answer this When you sample, what bias are you inflicting? How do you control for biases? What are some of the first things that come to ...
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28 views

How to compute bias mean squared error and standard error in penalized logistic regression

I am working on my Ph.D. research on penalized logistic regression. In my simulation using R, I have run the following code: ...
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1answer
86 views

How do AR,ARMA,ARDL and other time series models correct for omitted variable bias

I have come across numerous papers that use an Auto Regressive Distributed Lag (ARDL) model of the following form: $$ \Delta y_{t}=\alpha_{0}+\beta_1\Delta y_{t-1}+\beta_2\Delta ...
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1answer
26 views

using unlabaled data in a classification problem (There is labeled data but it comes from a biased sample)

I have a binary classification problem. The task is to rank instances from high probability of fraud to low probability of fraud. The following data is available: ~7.000 instances of 0/1 labeled ...
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Where is the maximum bias and variance in a histogram as non-parametric density estimator?

I am a little bit confused about bias and variance of non-parametric density estimators and hope you can help me. Assuming a constant bandwidth and sample size, I am wondering at which points of the ...
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Classification: odds of two totally biased classifiers

In a binary classification scenario, is it a sound approach, if I built two separate classifiers which are each trained only on a single class (positive and negative strictly separated) -- thus ...
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36 views

Estimating the true distributions from a sample of distributions

I am having a hard time formulating the following problem. Consider a company that runs a survey across several cities in the US to estimate the percentage of right-handed people and left-handed ...
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Conceptual question about bias of an estimator

I cannot see the notion of 'bias' of an estimator in a statistical model clearly. Here is my concern: Let $(Y,X)$ be a training data set. I generate this dataset according to the model ...
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38 views

How to correct heteroskedasticity in linear model of probability?

If we fit linear regression model to data, where dependent variable is binary response, then heteroskedasticity occours, how to correct for this issue ? Is it different then correcting for ...
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Comparing the Magnitude of the Difference in Variances Between Groups to Identify Selection Bias

I'm comparing two populations--private and public sector accounting firms in the state of Rhode Island--for differences in the distribution of quality/ability of the accountants who work at those ...
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17 views

Bias on many variables

Question: How to weight a sample to remove bias that is seen on many variables? Background: I've got two samples which are not random. For every individual I've got three categorical characteristics ...
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42 views

Meta-analysis: Difference between direct and indirect restriction of range

Looking at meta-analysis for personnel selection procedures, I am having really big troubles to figure out the difference between concepts of direct restriction of range (DRR) and indirect restriction ...
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72 views

Causal links with omitted variables

So I have a fairly basic setup, with $X\rightarrow Y$. However, I've run across a potential third variable, Z, that is probably correlated with both X and Y. However, the causality for Z is unusual ...
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2answers
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Can 'selection bias' refer to bias in the intervention as well as in the sampling?

I have been using the term selection bias to refer to a situation where (e.g.) schools with certain pre-existing characteristics are more likely to be included in (e.g.) a teacher training programme ...
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27 views

removing batch effect when combing patient's data into a large cohort

I have some clinical data quantifying severity of disease for patients from 3 different hospitals. Basically, the patient severity vector for each hospital looks like below: ...
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Bias/variance tradeoff tutorial

I'm looking for a good tutorial about bias/variance tradeoff. In particular, I'd like to find someone that explains how different algorithms in machine learning play in this tradeoff, and possibly how ...
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Definition of bias for f-hat: Why do we take the expected value?

From Wikipedia: $$ Bias(\hat{f}(x))^2 = E[f(x) - E[\hat{f}(x)]]^2 $$ $\hat{f}$ is our estimate of $f$, and the expectation ranges over different choices of the training set. The same page also ...
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Bootstrap: estimate is outside of confidence interval

I did a bootstrapping with a mixed model (several variables with interaction and one random variable). I got this result (only partial): ...
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Quantifying 'survey bias' in reports

In situations where you know the individuals answering the survey are suspectible to some sort of bias within their responses, is there a way to simply integrate it into inferences made about the ...
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1answer
44 views

K-fold validation, how to use MSE and STD for model selection

When using K-fold validation for model selection I'm wondering what's the best approach to select a model using both the mean square error (MSE) and the standard deviation of errors among folds (STD). ...
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1answer
24 views

What to do about very unstable mixed-effects models

I'm working on some poisson mixed effects models for an interrupted time series analysis, and I'm running into two frequent errors. The first I've posted on Stack Overflow, as it appears to be purely ...
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1answer
74 views

Self Selection bias for estimating a valiable correlated to the selector

I am trying to find a way to see if a measured variable between two groups is significantly different. This would normally be done through a t-test if the two groups were randomly selected from the ...
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1answer
39 views

Question about posterior mean calibration

I'm reading the article "Prior distributions for variance parameters in hierarchical models" by Andrew Gelman(link). This is an extract that I don't understand very well: Posterior inferences can ...
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1answer
99 views

Finding an unbiased estimator with the smallest variance

I will state the question then my methodology. Q: We have 3 random variables, $X1,X2,X3$ that are independent and identically distributed (iid). We would like to estimate $\theta = E[X1]$. Suppose ...
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1answer
93 views

intercept bias in logistic case-control regression: which is the reason?

I don't understand the reason why if I use case-control sampling in a logistic regression then the intercept is biased. The book Agresti 2007 (An introduction to categorical data analysis) says: ...
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What happens under the coexistence of biased estimation and multicollinearity?

I understand that multicollinearity induces inflated standard errors but doesnt bias coefficients while error-correlated omitted variables biases coefficient but what happens under the coexistence of ...
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When is the bootstrap estimate of bias valid?

It is often claimed that bootstrapping can provide an estimate of the bias in an estimator. If $\hat t$ is the estimate for some statistic, and $\tilde t_i$ are the bootstrap replicas (with ...
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1answer
38 views

Quadratic mean convergence of a biased coin using conditional expectation

I'm a master's degree student and after a lot of research and some days trying I still can't get the answer for a question proposed by my Statistics professor. He asks to toss a coin with a random ...
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11 views

Dealing with gender bias in Clinical Field Study - non parametric data

I have 105 patients to compare to 191 non-patients, across numerous non-parametric variables. However, my key confound is gender: 60% male in the patient group and 35% male in the non-patient ...
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Paper showing that logistic regression intercept biased in rare events

I'm studying the logistic regression for estimate the Probability of Default of SME's. Fortunately the event (firm's default) is a rare event. King and Zeng tell us that "logistic regression can ...
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Biasing SkLearn Algorithms to Positive Outcomes

I am trying to run multinomial naive bayes on a series of examples in python using sci kit learn. I am consitently getting all examples classified as negative. (The ratio of positives to negatives in ...