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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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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15 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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77 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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27 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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1answer
48 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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35 views

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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343 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
117 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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92 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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101 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
44 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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20 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
101 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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140 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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34 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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24 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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1answer
57 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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72 views

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) ...
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Unbiased Estimator of Days Until Completion?

I'm trying to get an estimate of average number of days until some event occurs (the event is guaranteed to eventually occur). I have some sample where this event has already occured for most ...
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26 views

Selection bias correction and a multinomial logit

I have a data set for a number of people making 2 decisions - where to live; and how many hours to work. For every observation with a non-zero amount of work, there is an observed wage. I've assigned ...
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13 views

Exposure classification bias, post-modeling

I am building a high-dimensional Bayesian spike-and-slab model to study the association between several organic compounds and a continuous outcome. The goal is to select the most influential compounds ...
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28 views

Down-sampling with building models (specifically random forests)

I was wondering if anyone had ever used down-sampling to build random forests with data that has unbalanced classes. Basically down-sampling samples (with replacement) x*min from the population where ...
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63 views

Calculating Bias from bivariate data

My data consists of one column of real temperature, and one column of calculated temperatures. I want a single number which quantifies the 'bias' in the real temperatures. Basically, if most of my ...
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37 views

Where did the words bias and variance come from? [closed]

I understand that a bias model is more relaxed while a model with a lot of variance is more flexible. but, where did these terms come from, and, why 'bias' and why 'variance'?
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Does lots of bias==underfitting, while lots of variance==overfitting?

From what I understand, there is a relationship between bias and underfitting; as well as variance and overfitting. Is a 'biased model' another word for an 'underfitted model'? Likewise, is a ...
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48 views

Bias Variance tradeoff from a Bayesian perspective

I know the general question about bias variance has been asked before. I understand the frequentist approach and the concept of model selection and the impact of bias and variance on "accuracy" of a ...
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1answer
411 views

Bias of the maximum likelihood estimator of an exponential distribution

The maximum likelihood estimator of an exponential distribution $f(x, \lambda) = \lambda e^{-\lambda x}$ is $\lambda_{MLE} = \frac {n} {\sum x_i}$; I know how to derive that by find the derivative of ...
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2answers
100 views

How to check if a random sample is biased

A question on how to prove that differences in mean value are statictically significant, and not just random noise. I have a set of two observations, one of which I'm going to deliberately bias like ...
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2answers
85 views

explanatory variables may bias predictions

I' m asking this question out of sheer curiosity, my teacher was not able to explain it. If I'm using logistic regression with categorical variables they are coded like {1,2,3}. I guess it wouldn't ...
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1answer
114 views

Differential baseline bias vs Heterogenous treatment effect

Where it says 'Differential baseline bias only', I see both a differential baseline bias and a differential treatment effect bias. From my understanding, to have no differential treatment effect bias, ...
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1answer
79 views

Is it possible for a regression to have the right functional form but still suffer from omitted variable bias?

Suppose that $$ Y = b + aX + e$$ where you know that $E[Y|X] = b + aX$. Is it true that the model cannot suffer from omitted variable bias? If this is true, then it follows that omitted variable ...
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75 views

Selection correction variable (non-randomly selected sample / bias) and Cox regression

I found an approach to calculate a selection correction variable for a Cox regression (Lee 1983. Generalized econometric models with selectivity. Econometrica 51: 507–512.): $$ λ = \phi \frac{ ...
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66 views

AR process with a constant

I am having trouble understanding the estimation of an AR process. In some textbooks, the AR(1) process is defined as follows: $y_{t}=\theta y_{t-1}+ϵ_t$ (which does not contain a constant). So the ...
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66 views

Bias Variance Decomposition for Mean Absolute Error

The mean squared error of an estimator $\hat{\theta}$ with respect to an unknown parameter $\theta$ is defined as $$ MSE(\hat{\theta})=E[(\hat{\theta}-\theta)^{2}]. $$ It is well known that there is ...
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98 views

Model fit is High but Ramsey RESET Test suggests omitted variables. What to do?

I'm trying to figure out what next steps to take. I created a model and ran OLS on a very large sample of data (over 400000 observations) and got an R-squared value of 0.80. So the model fit seems ...
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1answer
78 views

bias and variance of correlation estimator

I calculated the bias and variance of sample mean $\hat{\mu}$ and sample variance $\hat{\sigma}^2$ but I could not calculate the bias and variance for sample correlation $\hat{\rho}$. How can I do the ...
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1answer
76 views

Bias of more than one endogenous variables

I may have a model with omitted variables that are correlated with my predictor variables. If I have in my model, let's say, two endogeneous variables X1, X2, but I am interested in obtaining an ...
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65 views

diagnosing bias, variance from learning curve

I was doing machine learning course at coursera and there was a lecture about diagnosing high bias, or high variance from learning curves. If anyone interested here is the lecture - ...
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43 views

Comparing two distributions with different biased sampling criteria

Suppose you are running an experiment with two conditions, A and B. At the beginning of the experiment, both populations are the ...
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20 views

Drawing a conclusion from data without a correlation to other supporting data

I am looking for the word/phrase that is used to say that a (potential) erroneous conclusion has been drawn from data without having a correlation to other supporting data points. For example, if ...
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93 views

Can something show bias but not be significant?

I was reading a research paper and read this statement: ...
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61 views

Simulating a bimodal biased IV estimator

How can I simulate a bimodal biased IV estimator? The common unimodal heavy-tailed biased estimator would be something like this: ...
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36 views

R packages that work with biased samples

I'm working with a biased sample of web users. I'm only able to track responses of users who have navigated my site in a certain way, and I'd like to run an analysis to determine how certain factors ...
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1answer
69 views

Does BIAS equal to MEAN ERROR

Bias is defined as an average of all errors (without abs) and this is, IMO, what I want. However, I have been asked to give MEAN ERROR. Is this the same than bias and is it wrong to call bias as mean ...
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38 views

Forecasting and auto-correlation [duplicate]

I'm reading this chapter forecasting principles and practise from a forecasting book. The author has explained a linear regression model. Now this linear regression model will definitely have some ...
5
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1answer
159 views

statistical handling of lab values below limit of quantitation (BLQ)

There were several samples BLQ because of the lower limit of quantitation (LLQ) of the method, e.g. 5 ng/ml or less. Using the statistical program PRISM6 I marked these values together with the ...
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64 views

Comparison between normal glm and glm.nb regression with quadratic term?

Let's say I have a function to simulate data for negative binomial regression: ...
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165 views

How do instrumental variables address selection bias?

I'm wondering how an instrumental variable addresses selection bias in regression. Here's the example I'm chewing on: In Mostly Harmless Econometrics, the authors discuss an IV regression relating ...
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Calculating Bias from Cox PH model

I am using COX PH model to fit a lifetime data set and estimating parameters. By the by I am also simulating data and trying to find out estimates of parameters. Now I want to calculate bias and ...