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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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1answer
31 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
32 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 ...
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0answers
8 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. ...
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1answer
9 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, ...
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0answers
14 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
16 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
25 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
13 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 ...
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0answers
26 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 ...
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0answers
13 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 ...
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0answers
34 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 ...
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0answers
7 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
26 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
103 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 ...
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0answers
16 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)= ∑ 𝑦𝑖 *log 𝑝(𝑥i)+(1−...
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1answer
61 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 ...
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0answers
12 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 ...
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1answer
50 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
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1answer
36 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 ...
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0answers
26 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.
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0answers
14 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} ...
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0answers
16 views

Possible increase/decrease in effect of omitted variable bias when transforming the dependent variable

We have estimated four different dif-in-dif models (two level-levels and two log-levels), and an important coefficient in one of the log-level models has changed sign. This variable was never ...
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2answers
38 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 ...
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1answer
35 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 ...
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0answers
68 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
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1answer
41 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 ...
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1answer
23 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....
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0answers
36 views

Bias and over-fitting in Maximum Likelihood estimation

In his book, "Pattern recognition and Machine learning", Bishop talks about the influence of the bias and overfitting in the MLE framework. Here is a quote from p.28, just before he has shown that the ...
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0answers
51 views

Cross validation and the Bias Variance trade-off

So I know that there have been a lot of questions about this topic but I try to understand it from a bit more theoretical/mathematical point of view. I have some basic questions of how cross-...
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1answer
232 views

Ramsey's reset test (i.e. Omitted variable bias test) result interpretation

I have the Ramsey's reset test result to find whether my regression has any omitted variable bias. I have the following result and shall I say I do or do not have omitted variable bias and why? ...
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0answers
23 views

Unbiasedness and consistency

Assume the simple regression model satisfying all Gauss-Markov assumptions. Somebody suggests the estimator Why may someone consider such an estimator? Why will this estimator be consistent? Why ...
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1answer
16 views

bias estimating the proportion in pooled population

Assuming we want to estimate the proportion of success and there are two stages. We will move to stage 2 only when the number of success is greater than equal to a threshold (say 5) in stage 1. And we ...
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0answers
54 views

Relationship between Total Over/Under scores and actual total scores in sports

I have a data set of actual scores from sporting games, matched with the bookmaker's Total Over/Under Score (O/U Score) and the odds the bookmaker was offering that the game's total score would fall ...
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0answers
17 views

Bias of the eigenvalues of sample covariance matrix

Consider and i.i.d sample $X_1, \ldots X_n$ in $\mathbb{R}^p$ with covariance matrix $\Sigma \in \mathbb R^{p\times p}$ What is the expectation of the eigenvalues of the sample covariance matrix?. ...
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1answer
61 views

Is $\mathbb{E}(\exp(-\hat{\mu})) = \exp(-\mu)$, when $\mathbb{E}\hat{\mu}=\mu$?

Say I have a biased estimator for $\xi$, say $\hat{\xi}$. But what I know is $\mathbb{E}(\hat{\mu}) = \mu$(unbiased), and $\xi = \exp(-\mu)$. So I wish to do the following bypass. Is $\exp(-\hat{...
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2answers
634 views

Is a regression causal if there are no omitted variables?

A regression of $y$ on $x$ need not be causal if there are omitted variables which influence both $x$ and $y$. But if not for omitted variables and measurement error, is a regression causal? That is, ...
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0answers
21 views

Biasedness of ML estimators for an AR(p) process

Do you know any derivations (or references) which quantify the biasedness of ML estimators of an AR(p) process?
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0answers
41 views

Does Nickell bias matter in forecasting?

The context is longitudinal data, with $i$ indexing individuals and $t$ indexing time. The goal is predicting $y_{it}$ as a function of lags of $y$ as well as $\mathbf{X}$, which might include lags. ...
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1answer
83 views

Biasedness of Uniform Distribution MLE

How do I show that the maximum likelihood estimator for uniform distribution on $[0, \theta]$ for a random sample of size $n$ is biased? I've calculated the MLE as $\max_i\{X_i\}$. Intuitively, we ...
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0answers
21 views

Double Mendelian Randomization: Reasonableness & False Positive Concerns

I've been interested in mendelian randomizations (a form of instrument variable analyses) as a method for gaining insight into causal relationships between risk factors and outcomes. An example i ...
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1answer
29 views

OLS weight bias with binary outcome

The typical approach when you have a binary outcome variable is to use logistic regression. If you use OLS regression then it becomes easy to violate various assumptions (normality of residuals, ...
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0answers
59 views

Trying to understand the boot function and bias in R

I have the following code with the assistance of package "boot", it is very simple so I can learn and you can teach me more effectively: ...
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0answers
30 views

Compute Bias in ''real data''

I would like to compute the bias of the estimate given that $X_i$ are iid $Bern(0.5)$, so $\theta = 0.5$ As an estimator I use sample mean $\hat\theta = \sum_{i=1}^{n}X_i/n$ Here is the simulated ...
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1answer
22 views

can you trust the statistical control

I'm reading a paper that compares two vaccine types. THe people who got vaccine 1 are of lower SES and have more chronic conditions compared to those who got vaccine 2. Multivariate logistic reg was ...
6
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1answer
109 views

Comparison of variance between two samples with unequal sample size

The primary goal of my analysis is to compare the variability in the response variable, Blood Pressure, between sample1 and sample2. The secondary goal is to test for a difference in means. I do not ...
5
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1answer
55 views

The Bias of Incorrectly Fit Model in a Linear Regression Model

"Suppose that we have fit the straight-line regression model $\hat{y} = \hat{\beta_0} + \hat{\beta_1}x_1$ but the response is affected by a second variable $x_2$ such that the true regression function ...
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0answers
21 views

Comparing Model's Performance on the Train and Test Sets

I've developed a model that predicts a future value of a parameter for the next 72 hours (only 11 hours presented on the chart). I've obtained the hyperparameters for my model with use of ...
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0answers
35 views

Neural Network Bias updating during BackProp [closed]

Can it make sense to say that when I update the weights in a positive way in a neural network also the bias is updated in a positive way and that therefore the trend of weight and bias for the ...