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Questions tagged [bias]

The difference between the expected value of a parameter estimator & the true value of the parameter. Do NOT use this tag to refer to the [bias-term] / [bias-node] (ie the [intercept]).

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6answers
2k views

What does “Scientists rise up against statistical significance” mean? (Comment in Nature)

The title of the Comment in Nature Scientists rise up against statistical significance begins with: Valentin Amrhein, Sander Greenland, Blake McShane and more than 800 signatories call for an end ...
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2answers
55 views

Bias in parameter estimates for Cox proportional hazard model when covariates are collinear

For linear regression, if $y$ actually depends on two positively correlated covariates $x_1$ and $x_2$ (we can call it the true model), and if we only include one covariate, say $x_1$, in the ...
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1answer
12 views

Is attempting to discern gender discrimination in a distribution descriptive or inferential?

Let's say I have a given sample population $P$, that describes the traits of a group of people as a predictor variable, and whether or not they are CEOs as a response variable. I am trying to ...
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0answers
18 views

Do zero-inflated models induce selection bias?

Zero-inflated models (e.g., ZI poisson, ZI negative binomial, hurdle) assume two processes for the generation of the observed outcome variable: a process for deciding whether the outcome is zero or ...
0
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1answer
34 views

Does minimizing expected squared loss (MSE) result in an unbiased estimator?

I have heard that the estimator with the lowest expected squared loss (mean squared error) is not always unbiased, but I have also heard that the constant that minimizes the expected squared loss vs. ...
1
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0answers
10 views

Probability of detecting small bias in a die in the low confidence regime

We are given a biased $m$-sided die: one of the sides has probability $\frac{1}{m} + \gamma$ and all the rest have probability $\frac{1}{m} - \frac{\gamma}{m-1}$ each. The goal is to figure out which ...
0
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1answer
42 views

Can a biased but consistent estimator have a non zero convergent bias?

I understand that an estimator can be biased and yet consistent, and for me intuitivly in these cases the bias converge to zero as n goes to infinity, however can it be the case that the bias won't ...
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0answers
7 views

Manually zero bounding a metric before significance testing in an experiment

I’m trying to replicate the methodology described in this paper to improve the sensitivity of a significance test on a metric (number of purchases) in my experiment on an ecommerce website. In short, ...
2
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0answers
10 views

Visualization of unbiasedness of high dimensional paramter estimates

Assume a statistical model $f_{\theta}(X)$ that allows to estimate a parameter vector $\hat{\theta}\in \mathbb{R}^p$ from data $X$ and assume that $p$ is high dimensional (you may assume something ...
0
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1answer
33 views

Interpretation of Mean Square Error formula

This is a very basic question. I'm looking at a physical problem where one wants to estimate a parameter $\lambda$ of a system. Suppose I perform a measurement on the system. I call the (stochastic) ...
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0answers
38 views

What statistical tools are available to remove bias from a dataset?

Three managers report to me. They have done appraisal of staff under them giving them a percentage. I have to sign-off those ratings but I face two major issues: The managers have a certain way of ...
3
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2answers
61 views

Omitted Variable Bias & Multicollinearity: Why are the coefficient SEs smaller in the unbiased specification?

In Introductory Econometrics: A Modern Approach, Wooldridge writes the following regarding the omitted variable bias and its effect on the variance of the OLS estimator (x1 and x2 are correlated): ...
1
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1answer
31 views

Bootstrap based bias correction

Assume we have a probablistic model $f_{\theta}(x)$ and try to estimate the parameter $\theta$ based on data $x$ with some procedure that yields a biased estimator $$E[\hat{\theta}]=\theta + \eta,$$ ...
1
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1answer
31 views

Propensity score matching: bias adjustment

I'm using propensity score matching to match similar individuals. I.e., I first estimate a propensity score (the probability of treatment conditional on some set of variables) and then match on the ...
0
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0answers
20 views

Bias vector regularization in LSTM layer

Are there any scientific papers or articles on use of bias vector regularization for training LSTM models ( I am using Keras: https://github.com/keras-team/keras/blob/master/keras/layers/recurrent.py#...
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0answers
80 views

Logistic Regression and Omitted Variable Bias

I just want to confirm that I am understanding this correctly. So if logistic regression models have omitted variable bias, does that mean that I should discard any logistic regression models that ...
0
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1answer
25 views

Dependent variable with many zeros in a difference-in-differences model

There is a question with a similar title: How do I estimate a differences in differences model when the dependent variable has many zeros? However, mine is a little different. Let's assume I have a ...
2
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1answer
32 views

Modelling approach - tennis match predictions

I am working with a dataset about a fictitious type of sport which is fairly similar to tennis: One has to win 5 points to win a game, 4 games to win a set and 3 sets to win the match. However, there ...
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0answers
20 views

Are Poisson Regressions with Serial Correlation Biased or Inconsistent? (No Fixed Effects)

Let's say I've got panel data where a count outcome $y$ and continuous independent variable $x$ observed each time period $t=(1,2,...T)$ for each individual $i$. I am interested in how $x_{it}$ ...
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0answers
31 views

Bayesian analysis of multilevel model with lagged dependent variable

Currently, I am constructed a bayesian multilevel model to analyze a panel data set which now basically looks like the following: $y_{ijt} = \beta_{0ij} + X\beta + \epsilon_{ijt}$. So, now only a ...
7
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3answers
235 views

Using regression weights when $Y$ might be measured with bias

Suppose we observe data $Y, X$ and would like to fit a regression model for $\mathbf{E}[Y \,|\, X]$. Unfortunately, $Y$ is sometimes measured with a systematic bias (i.e. errors whose mean is nonzero)....
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0answers
27 views

Feature selection on training set without cross validation

I have a large dataset (1M+ samples) with 500 features. I need to create a predictive model that can be trained quickly. So, I want to perform an initial feature selection before building a classifier....
0
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1answer
41 views

On the bias of a confidence interval

I have that $n(\hat{f}(x)-f(x)) \sim N(\mu,\sigma)$ And $\mu$ cannot be estimated. Can I say that the bias of my confidence interval for $\hat{f}(x)$ is $\mu n^{-1} $?
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0answers
42 views

Are vanishing bias and variance enough for pointwise consistency for KDE-based estimation?

Question: Is the condition that asymptotic bias and asymptotic variance goes to zero for infinite samples sufficient to guarantee the pointwise consistency of an estimator based on plug-in kernel ...
0
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0answers
39 views

How to identify Post Treatment Bias?

I have a question about post-treatment bias. I'll use the following example: Let's say I created a multivariate regression model for how many points a basketball player will score at a given night. ...
1
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1answer
20 views

Do propensity score matching methods need to factor in the index date in a matched cohort context?

I am working on a comparative effectiveness study where we estimated the propensity of treatment between two groups and are exploring matching on the propensity score. The study period is long, ...
0
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0answers
20 views

Bias and Variance in underspecified models

Galit Shmueli (2012) introduces in her paper "To Explain or to Predict" the biases and variances of correctly and underspecified predictive models. The correct model is $f(x)=\beta_1x_1+\beta_2x_2+\...
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0answers
25 views

Bias correction when using loo cross-validation to replace unreliable PSIS-LOO estimates

The PSIS-LOO information criterion (see this paper by Vehtari, Gelman, and Gabry) assigns a Pareto shape parameter $\hat k$ to each observation in the data, and these $\hat k$ values can be used to ...
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3answers
30 views

Building a binary classifier on uncertain 0's

When building models to predict probability of sales etc. Its intuitive to select customers who already have bought the product as training data for class 1 and customers who does not have the product ...
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0answers
19 views

upward/downward bias of negative variable

If I have a variable that, considering some omitted factor, should have fallen by a higher amount than when it is not there - would that be a downward bias? I.e. the decrease is not large enough, so ...
0
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0answers
27 views

Why do we take `(Bias) ^2` in total error in a model? [duplicate]

I was recently studying some book and few blogs and come to note that : Total error = Bias^2 +Variance + irreducible error Also, I know that these are the errors ...
13
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8answers
4k views

How to treat illogical survey responses

I have submitted a survey to a sample of artists. One of the question was to indicate the percentage of income derived by: artistic activity, government support, private pension, activities not ...
0
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0answers
15 views

Poisson bias adjustment

So I was hoping someone could help me make sense of this problem. I came across this paper that discusses how the FSL probabilistic DTT may yield bias tractography relating to the physical distances ...
2
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0answers
38 views

Calibrating probabilities of a binary classifier when class prior is unknown

Is it possible to calibrate the probabilities of a binary classifier when the class priors are unknown? In cases where the data is obtained with selection bias (i.e. more positives than negatives in ...
0
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0answers
9 views

Log-linear BIAS adjustment

I have a loglinear model of: $log(\mu(S_{ij|gij}))=\alpha_0+\alpha_1g_{ij}$ where gij is distance, and Sij is connectivity There is a bias in the distribution of count values for the outcome ...
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0answers
42 views

Reducing Bias from a Random Forest - Feature Importance

I'm currently looking to show which of three variables is more important in classifying something as True or False. Everyone agrees that all three variables are important, but not all agreeing on what ...
3
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2answers
117 views

Independence of events in real-life data

Most of statistical methods (if not all) rely on independence of events. How do we know that this assumption is valid in real-life problems like clinical trials or web crawling? What might be the ...
0
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0answers
29 views

Biased coefficient estimates when using logistic regression with unbalanced classes?

I'm aware of the fact that probability estimates can be biased in logistic regression when dealing with unbalanced classes. When looking at the log-likelihood function ... $$ ℓ(β)= ∑ 𝑦_𝑖 *\log 𝑝(𝑥...
2
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1answer
77 views

Bias corrected calibration curve (regression modelling strategies)

I have a question regarding calibration plot for a binary logistic regression model (calibrate) in the rms(regression modelling strategies) package. The Bias-corrected curve (see below) shows if the ...
0
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0answers
15 views

Bias-corrected Property for Jackknife's Pseudo Values

I come across the following formula from a note, saying that we could think of jackknife as a bunch of independent pseudo values with the following form: The notes further comment that the sample ...
0
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1answer
53 views

arbitrariness in bootstrap bias estimation

The bootstrap estimates bias by applying the "plug-in" principle to $$E(\hat{\theta}_n) - \theta$$ I got this knowledge from p.124 of Efron, Tibshirani, 1994. equation(10.1) $\text{bias}_F=E_F[s(\...
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0answers
17 views

cumulative effect of near significant differences?

My knowledge of statistics is pretty limited at this point, so you'll have to excuse my ignorance. We've performed prospective randomised study looking at the differences in detection rates of cancer ...
4
votes
1answer
37 views

How to name a bias that is not quite the “immortality bias”

Strange question from me, but try to follow me. I do not remember or name correctly a type of bias in cohort study which is pretty clear in my mind. I try to explain: Let's assume that I want to test ...
0
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0answers
28 views

Which ML algorithms have a low bias (irrespective of variance)?

Is there a specific list of algorithms that tackle the bias problem well? This search doesn't seem to yield much on Google.
0
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0answers
16 views

Confidence interval with an unknown constant bias

Assume that we have an estimator $T_n$ of the parameter $\theta$ where $n$ is the sample size and there exists an unknown constant $C$ such that $\sqrt{n}(T_n-\theta) - C \overset{d}{\longrightarrow} ...
2
votes
2answers
43 views

Coin toss strategy [duplicate]

If we a sequence of 5 heads or 5 tails was unlikely, and given a strategy to wait for a sequence of 4 (e.g., 4H), and then bet on the opposite outcome on the 5th flip (e.g., T), is this a flawed ...
0
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1answer
37 views

Detect coin bias from observation

Is there a way to determine whether a coin is biased, using probability/statistics method, say the following two questions: if observe 8 heads in 10 flips, is the coin biased? Or if observed 3 ...
2
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0answers
88 views

What is the bias in PCA regression?

Assuming we have $n$ principal components and use $k<n$ for a linear regression. What is the bias of the l.s.e estimator $\hat \beta$ for the slope parameter using just these k components of the ...
4
votes
1answer
97 views

What causes exponential distribution to have biased and non-biased ML-estimator?

What causes exponential distribution to have biased and non-biased ML-estimator? $f(x;\theta)=\theta \exp(-\theta x)$ has biased estimator. $f(x;\theta)=\frac{1}{\beta} \exp(-x/\beta)$ has ...
1
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1answer
29 views

Linear regression of dependent variable squared & retransformation

I have performed linear regression of a dependent variable squared, & my statistics package produced least squares means for each level of categorical variables that I would like in original units....