Questions tagged [error]

The error of an estimate or prediction is its deviation from the true value, which may be unobservable (e.g., regression parameters), or observable (e.g., future realizations). Use the [error-message] tag to ask about software errors.

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Assumptions in Multiple linear regression [duplicate]

Is the following assumption in MLR (multiple linear regression) true or false ?? $\epsilon_i$ is independent of $Y_i$ for i=1,…,n. Where, $\epsilon_i$ is the random error in the model $Y_i$ is the ...
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When would you need scaled error between different time series evaluations?

Let's say we have 3 time series for three different fruits sales over one year. Although they are all fruits, their daily sold volume is very different. For example, imagine ...
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How to check assumptions of an AR(1) process

My question is, if a model allows the errors to follow an AR(1) process, how to check for the model adequacy? Can we use ACF and PACF plots?
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How can I derive OLS predicted error term ^ei as a function of ei?

First of all, I'd like to say that any kind of help would be really helpful, whether it's a hint or a good grad/undergrad book. Right now I'm working with Econometric Analysis of Cross Section and ...
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Strict exogeneity and AR(1) on the error term

I have a theoretical Fixed Effect GLS model (FEGLS) in which I assume that errors follow an AR(1) process. Below I describe the main model Now, notice that it is specified that the epsilon is ...
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Difference between residuals and idiosyncratic errors?

I have a simple question. I want to know the difference between the residuals obtained from a model and idiosyncratic errors.
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1answer
34 views

Empirical Risk Equal to True Error under condition

[Note: Crosspost from stackoverflow, I think I maybe should've started here] I've been working through "Understanding Machine Learning: From Theory to Algorithms", and on pg. 46, after the ...
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How to display error on a 2d median

Below is a 2d scatter plot where the large green dot is the median of the data in x and y. My question is about whether there is a convention for showing the error on the median. As shown, each of the ...
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Regularization and Shrinkage : Theoretical Advantages vs. Empirical Advantages

I have the following question about the theoretical advantages vs. the empirical advantages of regularization (i.e. shrinkage). As far as I understand, this is the general idea behind regularization: ...
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Explain the correlation between 7 critical success factors and 8 factors representing firms characteristics with ANOVA

For my dissertation I need to check if how 7 factors vary is somehow explained by how 24 other factors vary. (how the critical success factors (which are 7) vary is explained by the characteristics of ...
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Should residuals be equal (or unequal) in multigroup SEM when testing means?

What happens if I allow residual variances (and their correlations) to be freely estimated when testing multigroup differences in intercepts? I am comparing intercepts of my dependent variables (e.g., ...
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Variance of the response versus variance of the error term

My question is close to this one (and I have read other posts) but unfortunately, I did not manage to find my answer. In "An Introduction to statistical learning", page 65 I have read that: $...
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How AdaBoost will treat weak learners with certain errors?

I have to answer the following question and Im struggling: For each of the following cases, explain how AdaBoost will treat the weak learner $G_k$ with the weighted error $\text{err}_k(G_k, w_k) = \...
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How does the concept of random covariability compare between complexity theory and discrete estimation theory?

Given a pair of permutations of the integers between 1 and $n$, inclusive, one could compute both a metric of Fisher (parameter) information, like Spearman's rho, or a metric of conditional complexity,...
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Is there a principled approach to build a Bayesian Credible Interval across an entire survey instrument?

I am conducting an opt-in online survey (read: non-probability sampling). Frequently, surveys report Margin of Error (MOE), both for specific questions and for the entire survey instrument. I know ...
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Beta-regression allowing for correlation of the error terms

Good morning to everyone, I've a problem with beta-regression. In R exist a package "systemfit" that allow to fit regression (normal with identity link function) allowing for correlation of ...
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1answer
51 views

Reconstruction error in PCA?

I'm using PCA for a while, but recently I read about reconstruction error which I cannot understand... For example let's consider dataset consisting 5 variables: $X_1, X_2, X_3, X_4, X_5$. ...
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Why is the lower bound of the confidence interval of a model's error relatively constant compared to the upper bound? [closed]

I am interested in studying the effect of increasing data samples for a regression model on train error and test error. For this I have used 95% confidence intervals for different values of a sample ...
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R Error - Chi-squared approximation may be incorrect

I have a dataset with salary information in various companies. I'm testing whether Job Title and Gender are dependent/independent of each other. However I'm running into an approximation error ...
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Best Error Metric for Quantity Spread Estimation Accuracy

What is the best error metric for the accuracy of predicting how a fixed quantity is spread over several buckets? E.g. say there were 10 units that needed to be spread across three categories: ...
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Convergence and rescale error when running inverse gaussian GLMM

I am trying to analyse response times from a study on hormonal contraception and it's effect on RT in anagram and logic tasks with a mixed effects GLMM Response time is in seconds and varies from ...
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Statistical error in Simulation with random initial seed

I have a simulation which takes a parameter $a$ as input and uses random initialized weights. If I vary the seed for the random input but keep the paramter $a$ fixed, the simulation return changes. ...
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Why is it called the ‘error’ term?

In econometrics, why is the error term called the ‘error’ term? The myriad things it captures that influence the independent variable are not errors. They are valid real life phenomena. Is there any ...
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Is the Cross Validation Error more "Informative" compared to AIC, BIC and the Likelihood Test?

Is the Cross Validation Error more "Informative" compared to AIC, BIC and the Likelihood Test? As far as I understand: The Likelihood Test is used to determine : Given some data, is some ...
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How did Cross Validation become the "Golden Standard" of Measuring the Performance of Statistical Models?

I have the following question: How did Cross Validation become the "Golden Standard" of Measuring the Performance of Statistical Models? I understand the "logical appeal" of Cross ...
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RMSE estimation from model accuracy and RMSE of dependent variable

Given the two variables/measurements, which were used for building up the model (Random forest regressor), I would like to estimate an RMSE of the predictor variable/measurement against the "real&...
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Measuring errors of relative frequency distribution over a time series

I have 2 time series, in each I have the number of visits in a certain place - one is the real number, one is a processed sample. Since the real numbers are in xxK visits per week and the sample is in ...
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Estimating model performance using samples from test set

Question: Would sampling (with or without replacement??) from the test set of data, computing mean squared error (MSE) for each sample, and then computing the average and standard deviations of those ...
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47 views

How to compute (and use) a confidence interval for binary classification probabilities

I have a trained image classifier and 30 test images, 24 of which are classified correctly. With a decision boundary of 0.5, the remaining 6 images are misclassified as false positives. I'd like to ...
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Random Forest in R: how to get OOB error and interpret error.rate table

I run random forest (using package randomForest) on the classic titanic data. Here are the code and results. ...
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Finding the error variance

I have the following model with 23 observations (n = 23): $Y_{i}=\beta_{1}+\beta_{2} X_{2 i}+\beta_{3} X_{3 i}+\varepsilon_{i}$ and the following information which is available in the form of ...
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50 views

Standard error of a probability distribution

I have some random data, s measured on an experimental system. Due to experimental constraints, I can sample it 150,000 times in every shot. I am interested in the probability distribution, P(s) of ...
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Cross validation with two data sets

I have data gathered in two different ways and I'd like to see if a model trained with data gathered with method 1 can accurately predict data gathered with method 2. In order to get a baseline ...
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36 views

Worst case error variance

I need to create an upper and lower bound for the error variance, in linear regression or otherwise (state space models etc.). One way is to bootstrap confidence intervals, but that can be very ...
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Directly discarding big term in the proof of error propagation formula of variance from random variable $x$ to $f(x)$?

I read the error propagation formula scanario said that, the connection between the variance of a random variable $x$ and $f(x)$ is $\frac{var(f(x))}{|\partial_xf(x)|_{x=\bar{x}}|^2}=var(x)$. While I'...
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Misclassification: differential and non-differential random and systematic

How to identify if misclassification is differential and non-differential?? Also need help distinguishing between: Differential random Differential systematic Non-differential random Non-differential ...
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1answer
313 views

How to calculate Mean Squared Error when there are multiple observed y values for a single x value?

Given a data set where there exists multiple different observed y-values for a given x-value, how do I calculate Mean Squared Error? The formula implies that I subtract the predicted from a singular ...
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Question about mean squared error of a sum raised to the kth power

Let \begin{equation} Q = \sum_{i=1}^{n} \alpha_i \end{equation} be a sum that we want to estimate. Let us suppose we have an algorithm $\mathcal{A}$, outputting an estimate $\hat Q$, such that \begin{...
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33 views

Mean of values with individual random errors

I have 3 values and each of them have some random error to them. These values have no correlation with each other and neither do the errors. I want to find the mean of these values and the standard ...
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Neural network prediction gets worse when ground truth is close to the edges of output range

I am trying to use a simple neural network to predict numerical values of certain properties of sensor data (Somehow a regression problem). My network has only 1 output with Tanh activation, so output ...
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51 views

How does Michaud Resampling improve Mean-Variance Optimization?

Michaud Resampling claims to reduce estimation error through the following process: Step 1. Sample a mean vector and covariance matrix of returns from distribution of both centered at the original (...
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Is the following methodology to find the error metrics between the two curves technically sound?

I am comparing two curves, one of which is derived from physical experiment, while the latter is obtained from a simulation. The experimental curve was used to calibrate the simulation results. The ...
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The difference between total error, prediction error and fitted error via residual

Consider a regression model $Y=E(Y|X)+Prediction \ Error$ i.e $Prediction \ error = Y-E(Y|X)$. Now, define an estimate of the regression function $E(Y|X)=\hat{Y}+ Fitted \ error$ i.e. Fitted error = $...
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How to propagate error in a regression calculation

My dataset is shown below. In it, I have 4 time points (T0-T3) where I measure counts for n different samples as well as a control. From this, I calculated standard error for each sample with the ...
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1answer
19 views

Why is binning in Expected Calibration Error done the way it is?

I see the definition of expected calibration error being $$\sum_{m=1}^{M}\frac{|B_m|}{n}|accuracy(B_m)-confidence(B_m)|$$ Where $B_m$ represents a outputs of the model that predicted class $m$ in a ...
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44 views

Data split using model's error

For splitting of the data into train/test/val I use stratified sampling. Then I confirm that metadata distributions represent the original dataset well enough. I want to start considering error of the ...
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1answer
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Is $R^2$ or RMSE more important for determining the success of a neural network regression?

I have designed a neural network with two different choices of features. Neither feature set stands out as one trains a neural network that scores higher $R^2$ coefficient on test data whereas the ...
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2answers
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RStudio Binomial Test providing strange results

I am running a series of binomial tests for different trials. I ran 319 trials, and no matter the number of successes, my p-value is still < 2.2e-16. This includes when my trial had 0 successes. <...
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Is the F statistic value the same as the residual error term?

A guide for authors says that a residual error term must be included when data are analyzed using ANOVA. Does this mean including the F value and degrees of freedom? If not, then what does this mean?

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