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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9 views

Compare accuracy of a new light meter

I'm performing a study where i want to test the accuracy of a new light meter (A) againsta a standard calibrated and validated light meter (B) as a reference. I have measure different light ...
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0answers
13 views

Use of data not captured in a survey for survey glm model

A former statistician in my organization carried out a survey to understand customer satisfaction using stratified sampling. On arriving at the organization, I was interested in seeing how variables ...
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1answer
22 views

What statistical tool can be used to correct for differences in the amount of data an individual is evaluated on?

Let's say an individual gets a score (between 1 and 6) on different pieces of equipment in their department. For example, if I'm proficient at repairing a particular piece of equipment I will score ...
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1answer
10 views

RBM - What are visible and hidden biases?

Can someone explain to me what is a visible bias and what is a hidden bias in case of a Restricted Boltzmann Machine ? I know what is meant by biases but what is hidden and visible bias ? Does ...
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27 views

Bias of a Gaussian

Given a set of observations $X=(x_1,\ldots,x_n), x_i \in \mathbb{R}^d$, the maximum-likelihood Gaussian $\mathcal{N}(\mu,\Sigma)$ is given by $\mu = \bar{x}$ and $\Sigma = \widehat{\sigma}^2$, i.e., ...
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33 views

Bias-variance decomposition

In section 3.2 of Bishop's Pattern Recognition and Machine Learning, he discusses the bias-variance decomposition, stating that for a squared loss function, the expected loss can be decomposed into a ...
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0answers
10 views

Test to identify bias in staff recording data - some guidence please

I am involved in a project where staff observe items and record their observations on an input device (ipads in this case). The data set is quite large (+750,000 records). Staff record using radio ...
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15 views

Organizing a non biased election

The project We want to organize an open primary in France on LaPrimaire.org for the next presidential election. It answers two problems: the abstaining gathers the most vote at each election, and ...
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16 views

What kind of bias am I introducing when I include Validation set (kept for model selection) in Train data?

As usual, I have three sets of data: Train, Validation and Test. So I use train data for model selection, where I select the model which would perform best on validation data. After selecting the best ...
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25 views

Linear model with biased estimator

Consider a linear regression model. Suppose that the estimator $\hat{\beta}$ for the vector of the parameters of the model $\beta$ is, for some reasons, biased. As a consequence: ...
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20 views

Predict individual data from aggregated data

I'm trying to construct a model in order to establish a relation between the non performing loans of an specific bank and the non performing loans of the entire system. Since the data of the latter ...
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0answers
28 views

Calculating bias and variance in a LOESS fit

I have datasets that can form several different curvy patterns between the dependent and independent variables. The 'true' relationship likely depends on a large number of factors that aren't easily ...
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1answer
32 views

Training set error as an estimate of bias

In his machine learning lectures (1 min 30 sec), Andrew Ng seems to estimate the bias using the training set error. Why is it ok to do it? The definition of "bias" in machine learning (see wiki or ...
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53 views

Why does Variance add to Mean Squared Error in Bias-Variance Tradeoff?

I am having a difficulty understanding this concept, mentioned in the book An Introduction to Statistical Learning, chapter 2. It is mentioned that Expected MSE has 3 components: ...
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2answers
75 views

What is bias in Bias-Variance Tradeoff?

In the book An Introduction to Statistical Learning, chapter 2, it is mentioned that Expected MSE has 3 components: ...
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2answers
349 views

Problem with proof - why exponentially smoothed time series is biased

I'm working through the proof why the exponential smoothing is a biased estimator of a linear trend. The book is trying to describe the expected value of an exponentially smoothed time series. It's ...
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1answer
44 views

Selection bias in trees

In Applied Predictive Modeling by Kuhn and Johnson the authors write: Finally, these trees suffer from selection bias: predictors with a higher number of distinct values are favored over more ...
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0answers
18 views

Bias of an estimated Gaussian density

I have an iid sample, $X_1,\dots,X_N \in R^d$, from a multivariate normal density with mean $\mu$ and covariance matrix $\Sigma$. I am estimating the density $p(y) = N(y| \mu, \Sigma)$, using ...
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1answer
120 views

Bias vs reducible error

I encountered a question while learning: While doing a homework assignment, you fit a Linear Model to your data set. You are thinking about changing the Linear Model to a Quadratic one. ...
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0answers
29 views

Estimating Confidence Intervals

I have built a model that estimates the number of users who bought an item. I have data for two time periods, August 2015 and October 2015. I want to compare the number of users who purchased the item ...
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1answer
38 views

Calculating Median of Different Data Groups?

Bear with me here. I'm a newbie at this. Let's say we have this data : ...
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0answers
24 views

Is the inductive bias a prior?

Wikipedia defines it like this: The inductive bias (also known as learning bias) of a learning algorithm is the set of assumptions that the learner uses to predict outputs given inputs that it has ...
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0answers
13 views

Custom metric in Caret that puts more weight on bias

I am fitting a machine learning model that needs to have a low bias; variance is not as important. As such I would like to fit a model that places more weight on bias, than using the custom metric for ...
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1answer
337 views

Why does Daniel Wilks (2011) say that principal component regression “will be biased”?

In Statistical Methods in the Atmospheric Sciences, Daniel Wilks notes that multiple linear regression can lead to problems if there are very strong intercorrelations among the predictors (3rd ...
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37 views

Post-hoc correction of machine learning bias

I have been using a machine learning algorithm to predict a continuous variable, although am having an issue whereby whichever method I use, there is a systematic bias at low and high values of the ...
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0answers
18 views

How to correct for study bias in protein interaction data?

Interactions between proteins are crucial for the correct functioning of the living cell. That is why it is important to study protein interaction networks, detect hubs, leaves and network modules and ...
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0answers
10 views

Why did the coefficient of an independent variable changed after putting controls and interaction effects into the regression? [duplicate]

Does the correlation sign of the independent variables play a role for the change? Why one of my coefficients increased while the other one decreased? Can I explain the downward and upward bias that ...
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10 views

Best estimate of among groups variance with unequal within groups variances

Goal I have about 100,000 sets of groups. For each set, I would like to measure its among groups variance in order to then make comparisons among sets. Description for each set In each set, I have ...
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42 views

Incidental parameter problem

I always struggle to get the true essence of the incidental parameter problem. I read in several occasions that the fixed effects estimators of nonlinear panel data models can be severely biased ...
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21 views

Including principal components in linear models as unobserved batch variables

It is common practice in statistical genetics to adjust for principle components or latent factors by including them in the linear model you're interested in. This is most commonly done in eQTL ...
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0answers
22 views

Closed formula for D4 constant calculation? (Moving range chart constant)

I need to build a Moving Range Shewhart control chart given a series of observations. In short, I have to calculate the central line and the upper and lower limits as follows ...
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1answer
180 views

Is this an unbiased estimator?

I'm working in the following problem: Let X be a sample of size = 1 from a Poisson distribution with parameter $\lambda$, and let $h(\lambda) = e^{-3\lambda}$. a.) Check if $T = (-2)^X$ is an ...
5
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1answer
44 views

why is $1/n \sum_{i} (X_i -10)^2$ unbiased

Let $\{ X_1,X_2,...,X_n \}$ be n observations randomly drawn from normal distribution with mean $10$ and unknown variance. Prove that the estimator $1/n \sum_{i} (X_i -10)^2$ is unbiased. Why is this ...
3
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1answer
41 views

How can I prove that the f-statistic does not follow an F distribution in the context of step-wise regression?

There is a good number of threads about the deficiencies of step-wise regression, and particularly on the shortcomings of the partial F test as a tool for step selection. However I find it difficult ...
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26 views

Conceptual definition between randomness, representativeness and bias in sampling.

I was wondering if you can help me clarifying some concepts (if it is possible providing references to papers or books) that I will write in the form of ideas rather than questions. Consider this ...
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18 views

How to determine the variance of an autocorrelation estimator?

In reference to the hint: the calculated expected value from problem 2 was found to be: Where the variables changed slightly due to where the image was found, however l = h in the question, and r ...
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0answers
28 views

How to prove the unbiased and biased estimator of autocovariance function?

These two estimators are commonly referenced as sample autocovariance functions. I'm curious how you're to show the first is an unbiased estimator, while the second is a biased one. And how would ...
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0answers
14 views

how can I check the bias between two groups

I have a presentation at the firm... using the stata. I want to check is there any bias between unweighted mean and weighted mean. and I already calculated the means between them..by common method ...
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4answers
171 views

What is the difference between bias and inconsistency?

I am trying to learn about bias in simple linear regression. Specifically, I want to see what happens when the $cov(e,x) = 0$ assumption of the simple regression is violated. If this assumption is ...
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25 views

The variance of a biased estimator

This builds on an an earlier question from Math SE. I am just starting to learn about the simple regression model. In particular, I am trying to understand what happens to $\hat{\beta_1}$ when the ...
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0answers
39 views

R-squared and omitted variable bias

Suppose you have the model: $$ y_i=\alpha+\beta X_i + u_i $$ where $u_i = e_i + Z_i$ and ${\rm Cov}(X_i, Z_i) \ne 0$. Therefore, we know that $E[u_i|X_i] \ne 0$. Is the $R^2$ biased as well?
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26 views

Is bagging a free lunch w.r.t. generalization error?

Since bagging seems to reduce variance without increasing the size of the hypothesis set (I think), is it fair to say that it does not increase the bias? Therefore, in terms of out-of-sample error, it ...
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0answers
11 views

Bias-variance trade-off in multi task learning

We know bias-variance trade-off for the single task setting. I was wondering whether anybody can comment for multi task setting. I mean for instance, for the usual model where we estimate the response ...
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0answers
16 views

Median Pearson's r calculation with regards to p-value

Assume I do have a bunch of Pearson's r values (say 100) over some experiments with different sample size (sometimes in the 10000s, sometimes just a handful). For each of these Pearson's r values I do ...
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0answers
21 views

Treatment Effect Approach and Selection Bias

Suppose to have the National Health Interview Survey data (NHIS), the health status of the observed people as outcome $y_i$, which has got different potential outcomes on the basis of a treatment ...
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19 views

Placebo effect in randomized controlled trials (RCTs)

How does the number of intervention arms in a given RCT comparing several interventions to a placebo affect the placebo effect?
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81 views

Ratio estimators in sampling

It is intended to estimate the number of dead trees of certain species a forest reserve. The reserve is divided into 200 areas of 1.5 hectares. O number of dead trees is measured using aerial ...
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0answers
25 views

minority class resampling and classification accuracy inflation

I have a question whether resampling (with synthetic data) to fix uneven class distribution inflates classifier accuracy? I've used SMOTE algorithm to increase the number of instances in 4 minority ...
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2answers
31 views

Standardizing data (mean = 0, SD = 1) while avoiding look-ahead bias

I'm running a predictive model. Over 60 months, every month I get a median value from a data set. To avoid look-ahead bias, I can only use the current and prior median values found up until this ...
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1answer
47 views

Bias in bagged decision tree estimates of probability (classification)

As far as I understand it, random forests are as biased as any tree in the forest. Bagging a non-random forest (using all available variables at any given split) is unbiased -- bias in random forests ...