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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Literature on this kind of bias
Suppose I'm trying to investigate the lifespan distribution of light bulbs. The catch is that I can only observe each bulb at most $T$ time units. So if the bulb doesn't blow before $T$ I will not ...
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30 views
Unbiased estimate of the semi-partial correlation
Is the sample semi-partial correlation a biased estimate of the population semi-partial correlation?
If it is biased, what is an unbiased estimator of the population semi-partial correlation?
Are ...
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1answer
33 views
Detect bias in subset of Bernoulli processes
I'm looking for advice on the best method to use to answer this question.
General scenario:
We have multiple testing machines A,B,C,D etc. each tests a identical randomly selected part and provides ...
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1answer
34 views
What's the difference between bias in model error in regression?
Is model error the same as bias in regression? For example, if I construct data by $y_i=N^{\text{th}}$ degree polynomial plus uncorrelated noise, and do a regression with the $M^{\text{th}}$ degree ...
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0answers
28 views
Question about predictive bias - intercept and slope bias
I am slightly confused on how to determine a slope and intercept bias. I have an assignment where i am supposed to conduct a gender predictive validity bias analysis.
However, my lab handout and the ...
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0answers
18 views
Consequences of non-stationarity on panel regression estimates
What are the consequences of including a non-stationary variable on a panel regression's slope estimates and their standard error estimates?
I am thinking of both Pooled OLS and Entity Fixed Effects. ...
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1answer
88 views
What is an unbiased estimate of population R-square?
I am interested in getting an unbiased estimate of $R^2$ in a multiple linear regression.
On reflection, I can think of two different values that an unbiased estimate of $R^2$ might be trying to ...
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0answers
49 views
Estimator bias without a closed form?
Given a regression loss function $l(Z,\beta)=||Y-Z\beta||_2 + \lambda \beta^TD\beta + r(X,Z)$ where $X$ is the predictor matrix, I would like to estimate a $Z$ that minimizes the above loss in a ...
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4answers
239 views
Why must one trade off between bias and variance?
Apparently, a learning algorithm must make a trade off between bias and variance when producing a hypothesis. Bias means systematic deviation from data. Variance refers to the error due to ...
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2answers
59 views
Bias in Estimators of Lognormal
I am modelling a process distributed as a 2 parameter lognormal distribution; determining the parameters by maximum likelihood.
I have simulated the bias in the estimators (logmean and logsd) as well ...
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0answers
44 views
Unbiased estimator of weighted sum of two poisson variables
Suppose that $X_1$ and $X_2$ are two random variables sampled from a Poisson distribution with parameter $\mu$. Let $T_1=\bar{X}$ be the sample mean and let $T_2=(1/3)X_1 +(2/3)X_2$.
Are T1 and T2 ...
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1answer
113 views
significant difference between coefficients
What is the correct way to test for significant differences in parameter estimates in the following case:
I have a dependent variable (height for age) and a independent variable (household state ...
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1answer
333 views
Omitted variable bias in linear regression
I have a philosophical question regarding omitted variable bias.
We have the typical regression model (population model)
$$
Y= \beta_0 + \beta_1X_1 + ... + \beta_nX_n + \upsilon,
$$
where the ...
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0answers
61 views
How do I explain that software implemented model selection procedures should not be used unsupervised?
I know that people generally say that procedures which select a model based on information criterion lead to inconsistent model selections.
I read a paper by Leeb and Potscher (2005), MODEL SELECTION ...
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1answer
47 views
question about price-elasticity and endogenity
In Davidson & McKinnon - Estimation and Inference I read that in a competitive market which is always in equilibrium we observe:
$Q^d_t = Q^s_t = Q_t$
where $Q^d_t$ is the quantitiy of demand, ...
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1answer
83 views
How concerned should I be about the appropriateness of my prior?
As I understand it, selecting a prior provides something of a starting point for your analysis. From there, the distribution is shaped by the observed data. Obviously, the more data you observe, the ...
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1answer
32 views
Comparison of methods with bias
In a planned study where I am supposed to assist, the goal is to measure the agreement between on one hand the results from an activity measurement device and on the other self-reported values. Both ...
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1answer
215 views
Biased estimates when intercept is included in a linear regression
I am simulating 10000 data-sets, each of length 20, that follow an autoregressive model with lag 1, using the following code:
...
5
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1answer
207 views
Does Pearson correlation require removal of bivariate or univariate outliers?
Does the Pearson's correlation estimator require no bivariate outliers, or no outliers in each of two individual vectors of data? The answer will impact on how I winsorize outliers before calculating ...
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1answer
159 views
Multicollinearity in OLS
I am reading Greene's textbook Econometric Analysis where he says that, if there's multicollinearity, then:
Small changes in data lead to large swings in parameter estimates.
Coefficients have high ...
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0answers
106 views
What are the conditions where we can regress non-stationary variables?
Obviously there are certain spots where it's okay to include a non-stationary predictor variable in a linear regression model. For example, a dummy variable interacted with a stationary variable must ...
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0answers
71 views
“Rule of Thumb” method to adjust for overstatement bias on a likert scale
I have a relatively novice question which I have been attempting to peruse the literature for the past hour to address without much success.
I am attempting to test a product concept in a survey for ...
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1answer
62 views
Remove data starting before defined start date for survival analysis
I want to do survival analysis with a big data set.
The data collection started on 1997-01-01 and is still continuing yet.
However, episodes that started before ...
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3answers
324 views
Parameter estimation of exponential distribution with biased sampling
I want to calculate the parameter $\lambda$ of the exponential distribution $e^{-\lambda x}$ from a sample population taken out of this distribution under biased conditions. As far as I know, for a ...
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0answers
42 views
The bias of Zellner estimators in dynamic SUR models
I have been playing around with a seemingly unrelated regression (SUR) estimation. However, for dynamic SUR models it is known that -- analogous to the ARIMA case -- an OLS/GLS estimate is biased. For ...
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1answer
327 views
Looking for a OLS-Equation if one Regressor is correlated with the error
How can I express a OLS-Estimator if I know about the correlation i.e. I know that $E(x_i u_i)=\rho$ (I'm not looking for IV or 2SLS).
I'll explain my problem with an example:
In a simple problem $\ ...
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0answers
96 views
Non-response bias
I have the following question:
In a survey, a simple random sample of 1,000 households was drawn to
determine the distribution of household size in a city. Interviewers
were required to visit ...
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0answers
69 views
Is it OK to use the CLT to create a normal distribution where there is none?
I have some data that looks like this:
Procrastinator has come up with one good suggestion for how to test hypotheses under this distribution, but it relies on some guesswork to fit constants. I ...
2
votes
1answer
67 views
Factoring in self selection bias
I am hoping to use some self selection survey data (it's from those awful things that pop up on the start page of a website asking if you have 5 minutes to spare).
This is for business decision ...
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1answer
80 views
Confusion related to the bagging technique
I am having a bit of confusion. I was reading this paper where it explained that bagging technique greatly reduces variance and only slightly increases bias. I didn't get it how come it reduces ...
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1answer
152 views
Bias of variance/precision estimator using Gamma prior
Assume I have $N$ samples $x_1, \cdots, x_N$ from a Gaussian random variable $X\sim N(\mu, \sigma^2)$ where both $\mu$ and $\lambda = 1/\sigma^2$ are unknown.
If I apply MLE, I have $\mu_{MLE} = ...
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1answer
77 views
Learning Curves Example
I'm trying to find a full example of how to plot learning curves.
I watched Andrew Ng's ML class on Coursera and he mentions using learning curves to diagnose variance-bias issues.
My notes show ...
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votes
1answer
76 views
Correcting biased polling
Let's say I'm polling for a binary election in different states with known biases. Furthermore, let's say I only manage to poll only a small sample of people in each of these states. How would you ...
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136 views
Improving accuracy of total variance through variance components?
I'm following a measurement guidance that specifies a technique to improve the estimate of total variance by extracting individual variance components and performing a sum of squares. I'm not a ...
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1answer
171 views
Comparing structural equation models with multivariate non-normality
I am aware that multivariate non-normality in SEM can inflate the chi-square statistic and deflate standard errors of parameter estimates. I can deal with the latter (in AMOS) using bootstrapping ...
4
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1answer
139 views
What is the estimation bias of the top estimate in a list sorted by value?
Let's make the problem as simple as possible. Assume two related random variables, $X_1$ and $X_2$. On the basis of some data we estimate their true means $\mu_{X_1}$ and $\mu_{X_2}$ by sample means ...
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1answer
157 views
Using linear regression for bias correction
I have a predictor and the ground truth. I have found that I can use linear regression for bias correction, so instead of using the predictor's estimate directly, we can use the one obtained from the ...
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3answers
250 views
OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equation?
Suppose ${X_{it}},{Y_{it}}$ are time series with $X_{it}\sim N(0.1,1)$, ($\sigma^2(Y_{it}) = 1$ and $mean(Y_{it})$ is similar to that for $X_{it}$, but changes when the dummy = 1). and $t \in ...
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1answer
346 views
Correcting sample bias
I am studying the correlation of two observed variables (call them $A$ and $B$). the underlying distribution for $A$ is symmetric around $0$ (for sure), however in my sample I have $411$ observations ...
3
votes
1answer
119 views
Bias in classifier model selection
Say I have a set of classifier models, each generated using feature selection inside a repeated k-fold cross-validation. Each classifier model is generated using a different set of regularization ...
3
votes
1answer
100 views
When to use B'' or B''D as a measure of response bias?
I hope this is not a stupid question, but here it goes:
Based on information from Macmillan and Creelman's Detection Theory (2005) and Pallier's R-code that I found here, Computing discriminability ...
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1answer
58 views
What is bias in aerosol data?
I was reading this information related to aerosol, especially aerosol optical depth of the MISR and MODIS instruments. I didn't actually get what bias means in the context of the AOT retrievals of ...
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vote
1answer
528 views
What is bias correction?
I have seen many places where they have input/output datasets where they first create a linear regression line, correct the bias, and then only use that data for their model. I didn't get what this ...
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0answers
62 views
Biased variation of $\chi^2$ statistic?
I've found a variation of the $\chi^2$ statistic that looks like this:
$\chi^2 = \sum\limits_{i=1}^N\,\chi_i^2 = \sum\limits_{i=1}^N\,\frac{(\log m_{i}- \log n_{i})^2}{\sigma_{i}^2}$
where ...
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votes
1answer
256 views
How to correct for generated regressor bias?
Dear Stack Exchange heroes,
For my thesis I am writing a paper on the financial crisis. In my model, I use two regressions, which look like this:
$$CONF = α + β_1 DEF_t + β_2 DIV_t + β_3 INF_t + β_4 ...
2
votes
2answers
3k views
Conceptual understanding of root mean squared error and mean bias deviation
I would like to gain a conceptual understanding of Root Mean Squared Error (RMSE) and Mean Bias Deviation (MBD). Having calculated these measures for my own comparisons of data, I've often been ...
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votes
2answers
135 views
Can the ratio importance sampling estimate by made to be unbiased with resampling?
Consider approximating the following integral:
$$
\mathcal{Z} = \int h(x) \pi(x) dx
$$
Where $\pi$ is known only up to a normalizing constant, that is, $\pi(x) = \hat{\pi}(x)/\mathcal{Z}_\pi$. We can ...
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1answer
196 views
Time-Series Data and Omitted Variable Bias
I understand that ,usually, time-series studies do not aim to provide a causal explanation of anything but rather aim to forecast. In which case it does make sense that most time series studies aren't ...
2
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0answers
89 views
Generalized Linear Models and Curse of Dimensionality
I was wondering what happens to bias and variance of GLM estimates as dimensionality approaches the number of training data points? Specifically in Linear Regression and Poisson Regression?
I know ...
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votes
2answers
85 views
How do you assess for mode bias and scale effects when designing survey questionnaires? [closed]
We typically educate clients on the potential bias of one mode over another (online versus paper surveys for example) and the bias a scale can have when designing questionnaires. A client recently ...
