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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8 views

When on the same data and model an unbiased estimator and a biased estimator give similar values

There was a general consensus here that statements like I calculated Observed $R^2$ and Adjusted $R^2$, and they were pretty similar, suggesting only a small amount of bias in the Observed $R^2$ ...
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42 views

Heteroscedasticity and bias shown in residual plots, lme

I have been fitting a linear mixed-effect model. The residual plots are not desirable. I have found many posts telling me the first is heteroscedastic, and the second is biased. But I can't find info ...
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0answers
19 views

Bias of sample correlation for discrete distributions

Is there a proof showing the bias (or lack thereof) of the sample Pearson's correlation for discrete interval variables? In particular, I am interested in how such a proof handles the expected value ...
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1answer
38 views

Overspecification bias/ including too many variables to a regression model

This seems to be the general view in statistics community: If the regression model is overspecified (outcome 4), then the regression equation contains one or more redundant predictor ...
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0answers
37 views

Limits and biases in this scientific article? [closed]

QUESTION: What are the statistical limits and biases in this scientific article, which challenge its validity? THE ARTICLE: Efficacy of hepatitis A vaccine in prevention of secondary hepatitis A ...
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0answers
5 views

UMVUE for the sample version?

When we say in terms of PARAMETER, there does not exist UMVUE. But what about for the sample? That is, uniformly minimizing MSE$(\frac{1}{n}\sum{(\hat{y}-y_i)^{2}})$ estimator $\hat{y}$ such that ...
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0answers
12 views

In Random Forest, why IncNodePurity is biased?

I've seen this statement many times, however, I could not find an explicit demonstration of why IncNodePurity biased (actually, how does one define theoretical value of importance, is not so clear, ...
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0answers
23 views

Suppressor Effects when x1 and x2 are uncorrelated?

I've found this very comprehensive Thread about "Suppressor Effects when x1 and x2 are correlated" and the read the literature that was listed. As far as I understand, a suppressor effect can occur ...
2
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1answer
54 views

what is bias and variance of an estimator?

I know what Variance is. But what is Bias? I just have problems to understand this what is written!
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1answer
47 views

Bivariate probit model with sample selection

Could you please provide an example and explanation why to use the bivariate probit model with sample selection? In this context, to what sample selection bias refers to?
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2answers
902 views

When is a biased estimator preferable to unbiased one?

It's obvious many times why one prefers an unbiased estimator. But, are there any circumstances under which we might actually prefer a biased estimator over an unbiased one?
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0answers
18 views

Understanding multicollinearity and bias in coefficient estimates

In trying to better understand the effects of multicollinearity within the context of logistic regression, I have come across the following quote from Paul Allison's textbook: Although ...
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0answers
12 views

Cancelling roots in ARMA(1,1) with external regressors

I am trying to find out what cancelling roots would imply for the estimators of my external regressors in my ARMA(1,1) model. Unfortunately however I'm stuck in my final step since I'm insecure about ...
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12 views

Computing bias due to measurement error:

I'm currently doing an exercise and faced with the following question: We have the true form: $y_i=\beta_0 +\beta_1 d_i +u_i $ Where $d_i$ is a dummy variable. We have measured $d_i$ with ...
2
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0answers
19 views

Regression models with several samples of the same people

I am trying to implement some regression models with my data of 56 features x 1500 samples to fit a response variable of 1x1500 and I am hesitating about the statistical validity of what I am trying ...
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0answers
5 views

Correcting for season-length bias of Gini on win percentage

I made this plot to try and compare the competitiveness of the major US sports (NHL/NBA/MLB/NFL): Each point of a given color represents, for a given season, the Gini coefficient of the win ...
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0answers
15 views

Bias and precision in estimating species richness?

I would like to estimate the total number of unique species within a community (=richness, for instance two species: cat and dog) from a randomly drawn sample. I am wondering what is the sampling ...
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0answers
16 views

estimate the probability of randomly clicking answers in a survey [duplicate]

People are asked to choose their favorite color among 4 colors (e.g. red, green, blue, yellow) in a survey. Among m responses, x1 are red. If we know the proportion of people who choose answer ...
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31 views

unbiased estimate for household size

We have a population of N people. They live in households of varying sizes: 1, 2, 3, 4, etc. We are going to do a random telephone survey and ask them how big their household size is. What are the ...
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19 views

Notation for computing MSE confuses me?

I wish to compute MSE of my models. Say my data was generated from the following model: $y_i=f(x_i)+e_i$ where $e_i$ is some noise around the true relationship ...
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2answers
145 views

Is bias a property of the estimator, or of particular estimates?

As an example, I often encounter students who know that Observed $R^2$ is a biased estimator of Population $R^2$. Then, when writing up their reports, they say things like: "I calculated Observed ...
2
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1answer
62 views

Omitted variable bias and the constant term

For omitted variable bias to occur when a variable is left out of a regression, there is one axiom and one condition that must be fulfilled: (Axiom) By definition, the coefficient of the variable ...
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1answer
70 views

Proving that $y_t = \beta_1 x_t + \beta_2 y_{t-1} + u_t$ parameters are biased when $u_t$ is autocorrelated

How do you prove the result that for equation: $$y_t = \beta_1 x_t + \beta_2 y_{t-1} + u_t$$ the beta parameters are biased when $u_t$ is autocorrelated? In other words, that$$ \text{Cov}(u_t, ...
8
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1answer
330 views

Are tree estimators ALWAYS biased?

I'm doing a homework on Decision Trees, and one of the questions I have to answer is "Why are estimators built out of trees biased, and how does bagging help reduce their variance?". Now, I know that ...
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0answers
34 views

Why is bias “constant” in bias variance tradeoff derivation?

I know there are plenty of questions about the Bias/Variance tradeoff. I've been trying to derive it myself to build some intuition. I looked at the Wikipedia page, and I saw this: Notice where ...
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1answer
59 views

Is there an approximate correction for bias in correlating probability distribution estimates?

I'm computing the correlation between two probability distributions $P(x)$ and $Q(x)$ that I am measuring empirically. Call the estimates $S(x)$ and $T(x)$. The data is binned, so the estimates of the ...
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1answer
40 views

Controlling for biased audiences in online surveys

For a long time I have been meaning to set up a bunch of online surveys asking a whole range of social questions and publish the results. I am well aware that there are various difficulties to ...
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3answers
636 views

Do we really need to include “all relevant predictors?”

A basic assumption of using regression models for inference is that "all relevant predictors" have been included in the prediction equation. The rationale is that failure to include an important ...
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0answers
10 views

Bias and Expected Value of Residuals

If I am running an OLS regression is it always the case that the residuals sum to 0? Or, if there is a bias, for example, their exists endogeneity, then when I run the OLS regression the sum of the ...
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1answer
27 views

Role of the bias term in regression

I was trying to understand the role of the bias term in linear regression which is given by, y=w^T. phi(x)+b From what I understand it allows for any fixed ...
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0answers
8 views

Ratio of TPR and TNR as a measure of biasedness?

Can the ratio of true positive rate (TPR) and true negative rate (TNR) be considered as a measure of biasedness? For example, classifier a has a TPR of 0.6 and a TNR of 0.4, while classifier b has a ...
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0answers
12 views

How do I evaluate the impact of sample bias on the generalizability of my findings?

I am performing a regression analysis to identify predictors for my DV, using survey data. When comparing auxiliary information on my participants (in my case firm size and industry) to the available ...
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1answer
30 views

Understanding the bias variance trade-off of the regression function

If we take $\mu$ to be the true regression function, and we estimate $\mu$ by $\hat\mu$ from the available data, which is random, and therefore so is the estimate, which we may denote by $\hat M_n$ to ...
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2answers
72 views

Why isn't variance considered a bigger deal than bias?

In statistical literature, people say: Let's avoid making a biased estimator, that will mess things up! Why not avoid also having a varianced estimator? They should be treated the same.
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1answer
49 views

Are there two definitions of the word bias?

I hear the term bias being thrown around a lot in statistical literature. For example, By using mean-wise imputation, we are adding bias to our estimate. Another example, The ...
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0answers
34 views

Decomposition of average squared bias (in Elements of Statistical Learning)

I can't figure out how formula 7.14 on page 224 of The Elements of Statistical Learning is derived. Can anyone help me figure it out? $$\textrm{Average squared bias} = ...
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0answers
16 views

Solving for Bias in Simultaneous Equations Model without Instruments

Suppose you have the following structural equations where wage and status are determined simultaneously and you do not have any instruments for wage or status: $(1) \text{wage}_i = \alpha_w + ...
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21 views

Can PCA be used to reduce estimation error for covariance estimation?

One of the uses of factor models is to estimate covariance matrices. The reason why you might want to do this is to reduce the number of variables that you have to estimate and so avoid accumulating ...
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1answer
20 views

How to match a biased sample to a population?

I have a sample of people which is biased in age, gender, geography. I am trying to measure various continuous outcomes out of them. I have the census data to tell me the reality of the population ...
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1answer
43 views

Derive bias when AR(1) is approximated by MA(1)

Consider the MA(1) process: $$ y_t = \varepsilon_t + \theta_1 \varepsilon_{t-1} $$ where $\varepsilon$ is a white noise process with $\mathbb{E}(\varepsilon_t) = 0$ and ...
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0answers
28 views

Bias in the regression coefficients of a generalized linear model under MLE

Question: Are the regression coefficients of a generalized linear model biased when estimated through maximum likelihood? Imagine, we have a generalized linear model where $E[Y] = g^{-1}(\mu)$ for ...
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0answers
30 views

How does CausalImpact Prevent Overfitting

I'm using Google Research's Causal Impact package, and I'd like to understand more fully how the package prevents overfitting and selecting a bad batch of the covariates by chance. Here's the ...
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0answers
22 views

Truncated dependent variable caused by the researcher!

I created my own index for the study on firms. I am interested in using the index as the dependent variable. According to other statisticians, firms with less than 100 observations used to create the ...
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0answers
16 views

What is the trade-off in the bias-variance trade-off? [duplicate]

Let $\theta$ be a parameter and $\hat{\theta}$ be an estimator for $\theta$. I understand that the MSE of $\hat{\theta}$ can be decomposed into its bias and variance. That makes sense. What I don't ...
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12 views

Same error on all sets

My concern is the classification of data splitted into training, cross validation and test sets. By evaluating my model, the values of precision, recall, f-score and auroc are nearly the same for all ...
2
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0answers
59 views

Expectations of kernel density estimate

Suppose $X_{1},..., X_{n}$ are independent and identically distributed according to the probability density function $f$. Let ...
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0answers
27 views

Modeling bias in reviews of conference papers

An article in Science Magazine claims that A little bias in peer review scores can translate into big money, simulation finds . The paper referred to there is paywalled, though. Can anyone point me to ...
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1answer
43 views

Using Coefficients without Knowing the Estimation Method

This is probably a dumb question, and I assume the answer is no, but I have a list of variables and coefficients associated with a linear regression: ...
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7answers
3k views

What are the most common biases humans make when collecting or interpreting data?

I am an econ/stat major. I am aware that economists have tried to modify their assumptions about human behavior and rationality by identifying situations in which people don't behave rationally. For ...
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15 views

Correct shifted data

I have sensor reading that incorporates some time delays in its measurements, so that the measurement values of it are shifted from its ideal values (illustrated on the figure below). I have a set of ...