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.

learn more… | top users | synonyms

0
votes
0answers
10 views

“True values” of beta regression coefficients [on hold]

I simulated survival times, status and covariates for a Cox model. Now I would like to calculate the bias of regression coefficient estimates. But for this, i need the "true values" of beta regression ...
0
votes
0answers
14 views

bias of an estimator when the variable is categorical

I want to calculate the bias of the coefficient estimate (beta hat) in Cox regression. But for a categorized variable, for example using quantiles we define a variable with 4 categories, then the ...
0
votes
0answers
18 views

bias-variance tradeoff vs precision and recall

Can anyone explain the link between bias-variance tradeoff and precision-recall tradeoff. Are they effectively the same thing?
0
votes
0answers
6 views

Searching for a term for systematic, universal non-reporting in survey data

I am searching for a technical term to describe a situation I have run into my survey research and analyzing survey datasets. In experimental survey research, systematic under-reporting and ...
19
votes
2answers
206 views

confidence intervals' coverage with regularized estimates

Suppose I'm trying to estimate a large number of parameters from some high-dimensional data, using some kind of regularized estimates. The regularizer introduces some bias into the estimates, but it ...
2
votes
1answer
36 views

Precise definition of a 'biased sample'?

Is there a precise definition of what a biased sample is? Or is it just a somewhat loose notion used in everyday parlance, but which does not have a precise mathematical definition?
8
votes
2answers
167 views

Biased bootstrap: is it okay to center the CI around the observed statistic?

This is similar to Bootstrap: estimate is outside of confidence interval I have some data that represents counts of genotypes in a population. I want to estimate genetic diversity using Shannon's ...
0
votes
0answers
18 views

Bias terms in SVMs

I'm training multi-class classification models using linear SVMs - by learning binary one-vs-all classifiers for each class. To classify a test instance, I evaluate the following equation for each ...
1
vote
0answers
19 views

Bias and variance of amplitude estimator [closed]

I'd like to estimate the amplitude $a[n]$ of the following measured signal, $$ s[n] = a[n] \sin(\omega_0 T n + \phi ) + w[n] $$ where $w[n]$ is assumed to be unbiased Gaussian white noise with ...
0
votes
0answers
14 views

Transform SVM instance to ensure zero bias

I guess the title is self-explanatory, but here it goes. Is there a way to transform the input to an SVM (i.e. the data points) in order to obtain a solution with zero bias?
0
votes
2answers
54 views

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?
0
votes
0answers
20 views

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 ...
1
vote
0answers
22 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 ...
1
vote
0answers
33 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, $E(theta)\frac 1 2 - (\theta)\frac 1 2 = 0$, ...
0
votes
0answers
46 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 = ...
3
votes
1answer
60 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 ...
1
vote
0answers
23 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 ...
1
vote
2answers
37 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 ...
2
votes
0answers
28 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 ...
0
votes
0answers
65 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 ...
0
votes
1answer
24 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: ...
0
votes
0answers
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 ...
0
votes
0answers
62 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 ...
6
votes
2answers
79 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 = $X_1$% ...
0
votes
2answers
64 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 ...
1
vote
1answer
38 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. ...
0
votes
0answers
23 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 ...
1
vote
0answers
127 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. ...
0
votes
0answers
31 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 ...
0
votes
0answers
28 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 ...
0
votes
0answers
19 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 ...
0
votes
1answer
15 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 ...
5
votes
2answers
74 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 ...
5
votes
1answer
68 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 ...
2
votes
0answers
77 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 ...
1
vote
0answers
27 views

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, ...
2
votes
0answers
42 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 ...
2
votes
2answers
144 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 ...
0
votes
1answer
27 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 ...
0
votes
0answers
31 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 ...
0
votes
1answer
31 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 ...
1
vote
1answer
31 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 ...
1
vote
0answers
22 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 ...
0
votes
1answer
63 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 ...
0
votes
0answers
53 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: ...
2
votes
1answer
160 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 ...
1
vote
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 ...
2
votes
0answers
92 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 ...
0
votes
1answer
17 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 ...
1
vote
1answer
40 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 ...