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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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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28 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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18 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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8 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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51 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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26 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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81 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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1answer
27 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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35 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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26 views

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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31 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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2answers
228 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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24 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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43 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
72 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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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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117 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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186 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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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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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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174 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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35 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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1answer
66 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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78 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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34 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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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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32 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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73 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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38 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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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
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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
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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
87 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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124 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
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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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86 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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71 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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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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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 ...