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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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When is the bias of a statistic of the form a/n + b/n^2 + c/n^3 *

In many books the bias-correction of the Jackknife resampling method is being prooved under the assumption, that the bias has a special form, namely a/n + b/n^2 + c/n^3 * ... Sometimes it's written "...
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OLS basic doubt

In a multivariate OLS model : $ Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon$ My estimator for $\beta_1$ is given by which expression: $\hat \beta_1 = [X_1'X_1]^{-1} X_1'Y$ OR $\hat \...
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Interval Censoring and Ecological or Temporal Bias

I am trying to motivate a secondary analysis of a trial that had event related data. The primary study treated the data as an interrupted time series (ITS). I would like to justify using survival ...
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26 views

Estimate mean of a population with multiple samples when the individual sample mean is biased

I am working with datasets of grades going ~15 years back for different classes. I am trying to determine if there is a difference in the average grade for odd years compared to even years. There is a ...
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27 views

Bias of a test statistic

I have a test statistic $T$ that has a Gamma distribution $\Gamma(k, \theta)$. The problem is when I do a Monte carlo simulation for large sample sizes, the parameters of the empirical distribution ...
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1answer
27 views

If sample standard deviation is biased, why do we use it in typical mean tests? [duplicate]

If sample standard deviation is biased, why do we use it in typical mean tests? Why do we not use an unbiased estimator by dividing the sample standard deviation by C4?
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Estimating bias in linear regression and linear mixed model in R simulation

I want to run simulations to estimate bias in linear model and linear mixed model. The bias is E(beta)-beta where beta is the association between my X and Y. I generated my X variable from a normal ...
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26 views

Can any unbiased estimator be changed into a consistent estimator when estimating functions of the mean [closed]

For an i.i.d sequence of Random Variables $X_1, \dots, X_n$, each with mean $\mu = \mathbb E[X]$, the goal is to estimate some continuous function $f$ evaluated at the mean, $f[\mathbb E[X]]$. If ...
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Ramsey's RESET test vs Rainbow test for omitted variable bias tests

I am trying to provide some statistical proof about the omitted variable bias in my regression model. I have used the following two omitted variable bias tests for this purpose: (1) Ramsey's RESET ...
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1answer
23 views

How are variance and bias interpreted in relation to data sets

To interpret the bias we just need the training data and the test data, since it is the measure of how far off the predicted values are from the true values(test data). But, to understand the variance ...
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Bias and variance decomposition to estimate prediction

There are various ways that statisticians have come up for bias vs. variance decomposition in terms of prediction estimation. My question is this, how can one leverage or create a loss function based ...
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Direction of bias when changing from OLS to IV

If when using an instrumental variable it increases the size of the coefficient and changes the direction of the relationship compared to OLS --> what direction of bias does it suggest in the OLS ...
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Resampling technique to compare genetic diversity indices

I would like to know what would be the more appropriate way to compare two gene diversity indices by resampling or bootstrap methods. The data are as follows. In the first sample, I have 23 ...
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1answer
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Is the resulting function of plotting two variables imply that all other factors are being held constant?

Say, for instance, I plot two relationships (separately): (a) Share of income spent on food vs. household income; and (b) No. of houses in a unit vs. population of a city Then, for both (a) and (b),...
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1answer
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No need for bias term if data is standardised? Linear classification models

For linear classification models, e.g. perceptron, bias term allows to move separating hyperplane away from origin. If data is scattered around the zero does that mean that we don't need bias term?
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Interpreting $p$-values and Chi square when variables are added to a model in maximum likelihood estimation

I'm running a maximum likelihood estimation (probit) and I'm experimenting with adding additional variables, walking the bias-collinearity tightrope. Please could someone explain to me intuitively ...
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Is there a test for omitted variable bias?

I study finance and economics and every time i study an econometric study with OLS regression i wonder how the author can be sure of the non existance of omitted variable bias. I guess that in almost ...
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Estimating a VAR model via OLS

I am looking at Vilasuso (2001), who says that when using least-squares to estimate causality in mean, there is significant size distortion if the conditional variances are correlated. My question ...
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1answer
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why ridge regression only decreases slope and not increases it?

I was following the below example from 'StatQuest with Josh Starmer' youtube channel. The example is pretty simple: red line is the usual 'least squares' (for the red points), and the blue one is ...
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Is it possible to audit a machine learning system for bias?

More specifically, imagine we were examining a machine learning system for bias in a certain dimension and for simplicity sake it consists of a singular machine learning algorithm. Could we take that ...
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26 views

Correction of inflated p values

I have thousands of p-values and they are far from being uniform distributed - because of heavy pre-filtering (as an example, we can look at proportion test - if one cell value is less than X, people ...
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17 views

Can someone explain the difference of mean and linear bias in residual analysis?

I am struggling in understand the difference between mean and linear biased. What does it mean the a regression has mean biased or linear biased? How do I interpret it?
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Bias/variance of IV estimation

I'm studying IV estimation by myself and have some confusion about the basics. Let $y=X\beta_0 + u$ be a linear model with endogenous variable $X$, and $Z$ be an instrument, meaning that $Z$ and $u$ ...
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1answer
41 views

Including Collider Variables in Prediction

When the goal is to estimate a causal association between X and Y in the regression framework, one should not condition on (include as covariates) collider variables (common causes of both X and Y) ...
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How can statistics be used to avoid “Lending False Credibility To Decisions We've Already Made”

In light of this article Data Science Has Become About Lending False Credibility To Decisions We've Already Made published in Forbes, I would appreciate input from the statistical and data science ...
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Why is this estimator biased?

$X_{1},X_{2},..,X_{n}$ are iid $\sim Poisson(\mu)$ than the MLE for $\theta=e^{-\mu}$ is $\hat \theta =e^{-\bar x}$ Why is this considered to be biased for $\theta$? Is $E[\hat \theta]$ not $\theta$...
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Upwardly biased forecast results due to period of high demand: how to deal with this?

I'm currently working on a call-center forecasting project with some data limitations. Currently it is still a learning-project, and I started with simple OLS regressions. For the months 2016-12 to ...
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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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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
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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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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 ...
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1answer
44 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. ...
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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 ...
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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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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, ...
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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 ...
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1answer
37 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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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 ...
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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): ...
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1answer
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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 $$E[\hat{\theta}]=\theta + \eta,$$ ...
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1answer
41 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 ...
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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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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 ...
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1answer
37 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 ...
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1answer
49 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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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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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 ...
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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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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....
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1answer
46 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} $?