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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No regularisation term for bias unit in neural network

According to this tutorial on deep learning, weight decay (regularization) is not usually applied to the bias terms b why? What is significance (intuition) behind it?
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Expected distribution of Likert to test for bias

I have conducted a survey which included a Likert response question. My question is whether or not it is possible to conclude bias like extreme responding and acquiescence bias by looking at the ...
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19 views

variance and sample confused

When solving (b), is the variance $$ V\bigg(\frac 1 2 (x_1+x_2)\bigg) = \frac 1 4 V(x_1+x_2) = \frac 1 4 \big(v(x_1)+v(x_2)\big)= \frac 1 2 \sigma^2 $$ or should I divide the variance by the sample ...
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29 views

Estimator, unbiased or biased

I am having difficulty with this. My procedure for solving it is that $$ E(\theta)= \frac 1 2 E(X-0.1) + \frac 1 2 E(X+0.1) = \frac 1 2 $$ So, $E(theta)\frac 1 2 - (\theta)\frac 1 2 = 0$, ...
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40 views

how can I tell whether the estimator is biased or not

$X_i\sim N(\mu,\sigma^2)$. Two independent samples of size $n_1$ and $n_2$, with means $\bar{X}_1$ and $\bar{X}_2$. Two estimators of $\mu$ are proposed: $\hat{\mu}_a = ...
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45 views

Question about bias-variance tradeoff

I'm trying to understand the bias-variance tradeoff, the relationship between the bias of the estimator and the bias of the model, and the relationship between the variance of the estimator and the ...
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21 views

Name for phenomenon which causes bias in estimation of extreme percentiles of a distribution fitted to points with large error bars

I have a series of small numbers (say 25-45) of values which were generated, and each value has an uncertainty associated with it. I also have a theory that says these points are supposed to fit well ...
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25 views

In survey sampling, have calibration margins to be known (estimated with 0 variance)?

Calibration estimators in survey sampling (as defined by Deville and Särndal, and implemented for example in the SAS macro "Calmar") generalize many other calibration estimators, including ...
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21 views

Characterizing weak instruments bias with more than one endogenous variable

With a single endogenous variable, it is well known that a weak instrumental variable (or set of weak instrumental variables*) will bias 2SLS estimates toward OLS estimates. But how can one ...
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32 views

Bounding the bias of standard deviation estimate for stratified sampling (MC)

I cannot find an answer to this issue: in Monte Carlo runs, if one uses stratified sampling then the unknown bias of the variance estimator ( $\bar{\sigma}^2=\frac{1}{N}\sum{(y_i-\bar\mu_y)}$ where ...
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1answer
20 views

Statistic test when bias is not random

Is there a statistical test that I can use to say that there is bias in the result of my analysis but the bias only occurs at certain region. The scatter plot below probably will make more sense: ...
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18 views

Forecasting on data you influence?

I have a question about forecasting on data you influence, like trying to reach a specific (composite) sales target and pushing various components of the aggregate sales count in order to make each ...
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57 views

Residuals Diagnostics, transformation or non-linear model

I am struggling with my data (hit counts for multiple target detection trials) To start, it is heavily negatively skewed: 00000000000000000000000000000000000 ...
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76 views

Estimating bias in surveys

Say a company runs a survey across random N cities independently in some country estimating the fraction of males and females on each city. E.g.: Males = $X_1$% ...
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50 views

How to deal with 'cut-off' selection bias/sampling bias? (truncated distribution)

In short When measuring an outcome with a normal distribution, but whos mean is below the detection threshold, can you still make statements about differences between populations? Example Say I ...
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1answer
35 views

extrapolation and selection bias

I have a cohort of patient data. I have 100 Affected and 900 UnAffected I am reassessing one of the variables for each of the patients, however I can only do so for 90 Affected and 200 UnAffected. ...
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22 views

The mystic “true” bias (bootstrap-method)

This is a problem of understanding. That's why it doesn't include any formula. I have one big data set (n=83 Observations) and a small subdataset (n=15). With the small subdataset, I estimated the ...
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108 views

Summary of estimator properties (consistency, bias, sufficiency, etc.)

I've read about various properties of estimators, but I'm wondering if there's some source with a summary (maybe a list, table, or graphic) of the properties for different kinds of estimators. ...
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22 views

Is regression dilution bias avoided by using time-dependent predictors?

Regression dilution bias implies that even random measurement errors may bias the results by pushing the regression slope towards zero. Cross-sectional studies are particularly susceptible to ...
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21 views

Skellam Distribution with Dummies (Difference of two Poisson RV)

The difference of two Poisson distributed random variables follows a Skellam distribution. We know that a Maximum Likelihood estimation using Poisson distribution yields consistent estimates also in ...
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17 views

Controls sampled on confounding variable

Let's say I wanted to use logistic regression to analyze the effect of an exposure variable on a categorical outcome variable ("yes" or "no"). I believe there are two important confounding variables ...
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1answer
13 views

Estimating population mean when using biased sampling?

Say you had a sample of 50 items that was constructed by taking selecting values that were in the top 75% (not in the first quartile), and you had to take 61 items to find those 50 (11 were in the ...
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2answers
68 views

How can increasing the dimension increase the variance without increasing the bias in kNN?

My question is about understanding Figure 2.8 in The Elements of Statistical Learning (2nd edition). The topic of the section is how increasing dimension influence the bias/variance. I can roughly ...
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1answer
67 views

If $\operatorname{Var}\left(\epsilon_i\right) = h\left(X\right) \neq \sigma^2$, what can we know about $\operatorname{Var}\left(\hat{\beta}\right)$?

This question uses the derivations found here. The short version Consider a regression model. If the error variance is a known function of the data (rather than a constant), under what conditions ...
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64 views

Omitted Variable Bias in Linear Regression - Simulation

Is the following a reasonable illustration of the OVB problem? We build up fictional data around the regression line: $$y = 7.2 + 2.3 \, x_1 + 0.1 \, x_2 + 1.5 \, x_3 + 0.013 \, x_4 + eps$$ by ...
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Publication bias in meta-analysis of single observation studies

I have conducted a systematic review and lme model of 50 studies attempting to economically value ecological services (previously un-valued). These studies do not use data samples or observations, ...
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32 views

Bias Correction for Large Scale Logistic Regression with Rare Events

I have a large dataset constituted of many ad impressions. My dependent binary variable clicked describe whether or not the ad was clicked on. As you can expect, the number of clicks is about 1000x ...
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2answers
125 views

How to draw a representative sample from a biased portion of a sampling frame?

I have a question concerning sampling. We are planning a study in which we aim to draw conclusions about the relationship between different sources of research funding and academic impact (measured ...
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1answer
26 views

Contribution of a sample to cross validation error

I was wondering how to asses which sample in the data, during K fold cross-validation drives the bias that may be observed in the results. My training data consists of 40 samples. And I try to ...
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27 views

Inferring the bias of two types of coin

I would like to find the bias of a type of coin, when there is uncertainty about which kind of coin I am testing. The scenario is as follows, there are 2 mints in my neighbourhood that produce ...
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1answer
29 views

What do you mean by pollster bias in an election?

I came across harvards election poll data science question. I which they ask: Is there a pollster bias in presidential election polls? What exactly is a pollster bias? can some one explain it to me in ...
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1answer
30 views

Individual-specific error component in pooled OLS

I know that Pooled OLS is not efficient if there is existence of the individual-specific error component (one that doesn't vary over time) because the usual standard errors are incorrect and the tests ...
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19 views

Modeling change over time when response variable has different range and variance?

Some background: I am working with data from a large cohort study. My outcome is a measure of fine motor skills, and was adapted from a psychometrically validated instrument (the short version ...
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1answer
51 views

bias and sampling

This was an interview question I encountered. can some one answer this When you sample, what bias are you inflicting? How do you control for biases? What are some of the first things that come to ...
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35 views

How to compute bias mean squared error and standard error in penalized logistic regression

I am working on my Ph.D. research on penalized logistic regression. In my simulation using R, I have run the following code: ...
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1answer
118 views

How do AR,ARMA,ARDL and other time series models correct for omitted variable bias

I have come across numerous papers that use an Auto Regressive Distributed Lag (ARDL) model of the following form: $$ \Delta y_{t}=\alpha_{0}+\beta_1\Delta y_{t-1}+\beta_2\Delta ...
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1answer
28 views

using unlabaled data in a classification problem (There is labeled data but it comes from a biased sample)

I have a binary classification problem. The task is to rank instances from high probability of fraud to low probability of fraud. The following data is available: ~7.000 instances of 0/1 labeled ...
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78 views

Where is the maximum bias and variance in a histogram as non-parametric density estimator?

I am a little bit confused about bias and variance of non-parametric density estimators and hope you can help me. Assuming a constant bandwidth and sample size, I am wondering at which points of the ...
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1answer
13 views

Classification: odds of two totally biased classifiers

In a binary classification scenario, is it a sound approach, if I built two separate classifiers which are each trained only on a single class (positive and negative strictly separated) -- thus ...
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1answer
37 views

Estimating the true distributions from a sample of distributions

I am having a hard time formulating the following problem. Consider a company that runs a survey across several cities in the US to estimate the percentage of right-handed people and left-handed ...
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49 views

Conceptual question about bias of an estimator

I cannot see the notion of 'bias' of an estimator in a statistical model clearly. Here is my concern: Let $(Y,X)$ be a training data set. I generate this dataset according to the model ...
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1answer
40 views

How to correct heteroskedasticity in linear model of probability?

If we fit linear regression model to data, where dependent variable is binary response, then heteroskedasticity occours, how to correct for this issue ? Is it different then correcting for ...
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34 views

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 Rhode Island--for differences in the distribution of quality/ability of the accountants who work at those ...
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1answer
18 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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46 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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1answer
78 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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2answers
48 views

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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28 views

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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47 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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32 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 ...