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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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 Arizona--for differences in the distribution of academic ability of the accountants who work at those firms, ...
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14 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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33 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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57 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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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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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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21 views

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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17 views

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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15 views

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
23 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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21 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
53 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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30 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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70 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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59 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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238 views

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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34 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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29 views

Mixed logistic model with complete separation

I want am trying to produce a mixed logistic model but certain explanatory variables suffer from complete separation. I am aware that I need to either use exact logistic regression or a firth ...
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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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83 views

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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27 views

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 ...
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3answers
101 views

Correcting biased survey results

Knowing that a population sample (non-random) is biased in terms of its demographics, what are the best practices to correct for this issue? That is, let's say that I can attach an array of ...
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What's the bias of calculating the Kendall coefficient of correlation on a sample instead of whole population?

I am trying to calculate Kendall coefficient of correlation but my data.frame in R contains 6 mln observations and 17 variables. It is numerically hard for R to compute the estimator on a whole ...
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33 views

How do I incorporate the biases in my feed-forward neural network

I'm trying to implement a FFNN. I'm doing this as an excercise to understand how biases play a role in the classification. I trained a NN using a package in R with the inputs being 1..100 and the ...
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28 views

Experimental Design questions

I have a couple of questions regarding the procedures in an experiment. If I would like to test out two different drugs and the effect it has on the subject, why would it be a good idea to randomize ...
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38 views

Are LASSO regression predicted values also biased?

Since LASSO regression biases coefficients to reduce variance, aren't the predicted values also biased? In my case I am looking at fitted values from a predictive logistic regression model with LASSO ...
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A/B Test - Reset data measurements when changing audience size?

I'm running an A/B test that originally was exposed to 10% of my traffic (5% variant / 5% control); The test has performed well thus far, and I'm looking to expand the size of the traffic pool to 50% ...
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If we nonlinearly transform the LS estimates, will they still be unbiased estimates of the true value?

So this is an discussion which came up with a friend/colleague who is a physicist postdoc. He has a bunch of data $(x_i,y_i)$ and wants to fit it to the form $y=e^{ax}$. He uses (weighted) nonlinear ...
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33 views

When comparing variability between unequal samples, is there a way to correct for sample size?

I am trying to compare test measurements taken at three time points in a training paradigm. The data for each test consists of a number of durations in ms. The variable I'm interested in is the ...
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232 views

Does adjusting for superfluous variables bias OLS estimates?

The usual textbook treatment of adjusting for superfluous variables in OLS states that the estimator is still unbiased, but may have larger variance (see, for example, Greene, Econometric Analysis, ...
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33 views

selection bias correction based on multinomial logit

Can anyone please explain how to correct selection bias in the Ordinary Least Square model when independent variable (which is expected to have correlation with errors or creating endogeneity problem) ...
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88 views

Estimating the uncertainty of a bias and a scatter

I have one single set of observational data. Assuming I know the right answer for one property of this data set and then I use one tool to measure this quantity. To get an estimate of the amount of ...
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47 views

Neural Networks sigmoid activation with bias updates

I am trying to figure out if I am creating an artificial neural network using the sigmoid activation function and using bias correctly. I want one bias node to input to all hidden nodes with static ...
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83 views

A regression specification problem: what if one control variable is a function of another—does this cause any issues?

Suppose you run a regression: $y_i = \beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} + \epsilon_i$ but you believe that: $x_{i1} = f(x_{i2})$ will this cause any issues for your estimation and ...
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Bias-variance decomposition with sklearn BaggingRegressor

There is an example given on the Scikit-Learn site that compares the bias-variance decomposition of the rmse of a single SVR model against a bagging ensemble. Unfortunately, the data is being ...
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405 views

Bias in jury selection?

A friend is representing a client on appeal, after a criminal trial in which it appears that jury selection was racially biased. The jury pool consisted of 30 people, in 4 racial groups. The ...
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3answers
120 views

Is 'fair statistics' a thing?

Given that statistics can often be abused to deliberately present 'facts' to support a pre-existing viewpoint. (Lies, damned lies and statistics). And given confirmation bias. Is there an ...
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126 views

Kalman Filter to correct model simulation bias

I am working with a large scale deterministic model, which attempts to simulate CO2 emissions in different regions. When compared to historic data, the model output suffers from systematic biases. ...
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29 views

Bias in lagged dependent variable [duplicate]

$$ y_t = θy_{t−1} + u_t \\ t = 1,...,T; $$ I need to derive a formula for $y_t$ and show that $$ E\left[\frac{\Sigma y_{t-1}u_t}{ \Sigma(y_{t-1})^2}\right] \neq 0 $$
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294 views

Omitted variable bias in logistic regression vs. omitted variable bias in ordinary least squares regression

I have a question about omitted variable bias in logistic and linear regression. Say I omit some variables from a linear regression model. Pretend that those omitted variables are uncorrelated with ...
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1answer
46 views

Omitting a moderator

I'm wondering what the effect is if I don't include moderators in my model? Is this the same or different from an omitted variable bias? I am having a hard time grasping this conceptually. More ...
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1answer
26 views

Non-response bias (many waves, time span between waves not consistent)

I want to ask regarding non-response bias. I have sent my questionnaire on-line to SMEs in Malaysia. However, I have sent reminders many times (around 5 times). However, now I cannot recall when the ...
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1answer
110 views

Regression where the dependent variable is the difference between two correlated variables — bias and other issues to consider

I am interested in estimating a regression that looks like this: $(x_{1,i} - y_{i} )_{i} = x’_{i}*\beta + \epsilon_{i}$ (1) However, I am not sure if doing this—in this form—is appropriate. ...
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1answer
186 views

Weighted regression

I have a response variable, y.hat, that is an estimate of animal abundance. I know the standard error of y.hat. I'm skeptical ...
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36 views

Applied Analysis Question

I'm a newbie analyst and I'm facing a machine learning / regression problem which I cannot solve. The data I need to use in my analysis consists of information about press subscriptions of some ...
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25 views

Using glm(family = guassian) on data that is actually Poisson. Strange non-symmetrical bias

Let's say I want test the consequences of assuming a normally distributed response variable in a glm model when it is really Poisson. I simulate some data with some quadratic terms. ...
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74 views

What statistical method to correct systematic error in the output of a economic optimization model?

I am working with an economic optimization model which attempts to model the dynamics of a certain commodity market (prices, quantities, production etc.) for different frequencies (monthly, quarterly, ...
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What is statistical Bias?

I am asking this question in context to section 4.1 in this paper: security control methods for statistical Database (http://www.utdallas.edu/~muratk/courses/privacy08f_files/stat_database_sec.pdf) ...