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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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multiple linear regression error minimization

regression analysis in different statistical packages fits the best line by minimizing the error of the fit, the error term used by default is mostly MSE (mean square error), in another word, ...
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Finding the type II error given the type I error for a minimax decision rule with 0-1 loss

Assume a two world state ($\Omega=\left\{ \omega_{0},\omega_{1}\right\}$ ) scenario and that we are given the [continuous] ROC curve $\left\{ \left(\alpha\left(\theta\right),1-\beta\left(\theta\right)\...
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65 views

Errors and residuals in linear regression

I think in common literature about statstics the authors are often very imprecise when it comes to residuals and errors. So far, I could not work that difference out completely and therefore have ...
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24 views

Is the loss is the same as the error in deep learning?

Is the loss is the same as the error in deep learning? I feel it's the same but I'm maybe wong...
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Measuring predicitve accurateness relative to mean squared error

Imagine that $N$ agents try to predict t $k$ values $e_1, ..., e_K$, that differ in their 'predictability', i.e. some values are much easier to predict than other values. I am trying to define a ...
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9 views

Include standard error of values of an independent variable?

Values for one of my independent variables include reported standard errors. Is there some way to include these standard errors (of the values of the IV, not of its coefficient) in a regression model -...
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31 views

Error Term in Logistic Regression

I am trying to understand what the "error term" in logistic regression is. It's clear to me that the difference between the observed value and the predicted value with logistic regression will be 1 - ...
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27 views

Bias variance tradeoff when the estimated target function is also random

I'm interested to understand "bias variance tradeoff" notion in a different setting than usually presented. In a setting where target $f$ (see the map $f$ below) is a random map rather than ...
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Noise in ARIMA Model In-Sample Predictions

I am working on fitting some financial data into an ARIMA model to give me a forecast of the next time period. I am using pyramid's auto_arima function to get a ...
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What is the probability that sample variance decreases by adding random Gaussian noise to the variable?

If we assume WLOG that our variable X has mean zero (mean-centered), then this can be stated $Pr \bigg(\sum x^2 > \sum (x-n)^2 \bigg)$ for some random variable $n$ distributed under $N \sim N(0, \...
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14 views

Including error dependent on output in Gaussian Process Regression

I have a set of experimental data that I am trying to fit using Gaussian process regression (GPR) using Python's sklearn package. The only problem is that my data has an experimental standard ...
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41 views

Linear regression model, SCE,SCT,SCM and model's error

Could you please check if what I've done is correct? and how could I improve some of them? Thank you in advance. Suppose I have the following data (the original data its like 20 data with decimal ...
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Validation of error bars with Gaussian process regression

I have a set of noisy data that I am fitting using Gaussian process regression (GPR) with Python's sklearn package using the treatment found here. Below is an example where the error bars on the ...
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18 views

standard error- residuals

assume I am predicting home runs, assume all player bat the same number of times, so we can do this by total home runs, and not home run rate) from a player based on past experience. I have a linear ...
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Subscript error from blau's index using the “diversity” function in R [migrated]

I am trying to get the blau's index using the "diversity" function in R. However, I constantly get the error using the code and data I suppose to be ok as below. ...
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54 views

What error analysis was used here?

I have two curves: one is experimental and another is fitted to the first one, the error estimation for the goodness of fit was conducted by another person 10 years ago on those data, there was two ...
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55 views

Does this approach of performing predictive modeling make sense?

My company purchased software for forecasting orders. The software looks at all locations where a particular order came from and adds up all the location demands in each month. It then builds a ...
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14 views

Standard error of mean vs error propagation

I'm confused on how to correctly calculate the final uncertainty from averaging measurements that each have their own internal errors. Say I have 3 voltage measurements: (1.232 ± 0.001) V, (1.197 ± 0....
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39 views

Consistency of the estimator of the variance of the error

In the classical linear regression model, the estimator of the variance of the regression error is $s^2 = \frac{e'e}{n-k} = \frac{u'Mu}{n-k}$ where u is the error vector, e is the residual vector, and ...
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How to combine two different errors

I have an estimated spatial distribution of gas concentration and its ground truth, and I have compared them on account of two errors: (1) the global error or the error in the concentration values in ...
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26 views

Compute Bias in ''real data''

I would like to compute the bias of the estimate given that $X_i$ are iid $Bern(0.5)$, so $\theta = 0.5$ As an estimator I use sample mean $\hat\theta = \sum_{i=1}^{n}X_i/n$ Here is the simulated ...
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Cross-Correlation Propagation of Uncertainty

I would like to calculate the uncertainty of the cross-correlation of two functions (in two dimensions but even one-dimension is a great start). Experimentally, I have discrete values of f and g, and ...
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29 views

Computing standard errors after estimating mean and variance using MLE

I am trying to make estimates of mean and variance using MLE (Maximum Likelihood Estimate) for 1000 random samples following normal distribution. I started by generating random sample of size n = ...
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measure for prediction error in random forest regression

I would like to know, if there are recommended papers describing the use of methods and measures for computing the prediction error of random forest predictions. Should I use 10-fold cross validation? ...
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1answer
18 views

Using datapoint multiple times in error [closed]

For a simple regression problem, say I have a function $f = x^2 + ax$ and am using mean squared error as a loss function. In each calculation of mean squared error, each datapoint gets used twice (...
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Generalization of median, mean for L_p spaces for p different than 1,2

I find it fascinating that the mean and median both minimizing the a measure of error of a point estimate. The median $m_1$ is any (non-unique) $m \in \mathbb R$ which minimizes the $L_1$ norm $\int ...
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When model complexity goes up, why test error also goes up, instead of staying on a similar level?

When model complexity goes up, why test error also goes up, instead of staying on a similar level ? I feel this is countering the intuition that when you add random parameters to a model, it should ...
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Measuring error from regression results, is MSE appropriate here?

I used boosted regression trees on a dataset I was working on to predict how much a customer will spend in a given year. Here is a sample of the output: ...
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What does 'Error(var)' in ANOVAs with repeated measures means? How is it calculated?

I checked several tutorials, books and online resources, but still I do not know what 'Error(var)' in Anova with repeated measures come from? How is it calculated? I see that number of measures ...
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Merging point estimates and confidence intervals for 2+ proportions

I had couple questions about this topic Combining confidence intervals for a particular equation and was wondering if anyone can help? For calculating combined p, how is the formula in the original ...
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1answer
40 views

My neural network will run okay, but occasionally (every 1000) it provides an error. [closed]

I am using a neural network to forecast the direction of gold prices. I have created a neural network neuralnet within R. My programme runs well and i can get a prediction accuracy of about 51%. ...
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10 views

Can a global error be divided in half for an isolated element of it?

At first, sorry for the quite general title description. I really do not know how to describe it properly. I'm running a monte carlo simulation in which I study how many particles of a fixed initial ...
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Determining how far an actual value is from a predicted value as $x$ increases

Assume you have 5 $x$ values (1, 2, 3, 4, 5) and 5 $y$ values (1, 2, 1.3, 3.75, 2.25). From this you estimate a linear equation ...
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31 views

Minimize sum of squared errors or its mean

Is there any difference in minimizing the sum of squared errors in a linear regression model learning, compared to minimizing the mean of the sum of squared errors, apart from having easier math when ...
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26 views

How to demonstrate RMSE for time series in percentages

I am doing forecasting for a time-series problem, and have ended up with a RMSE of 3793.86. I then took the mean of all the rows available to me, saw that it was 275007.975. Is it correct to say ...
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Negative relative error

I am trying to calculate the relative error between one model and another as follows: (model1 - model2)/ (1 - model2) where ...
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1answer
52 views

Approximating the error of maximum likelihood estimation

I have a log likelihood function of a model and I want to find $\mu$ and $\sigma^2$ which maximize the log likelihood. Since the log lik function is quite complex, I decided to use Nelder-Mead ...
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Intuitive explanation for t vs z in confidence intervals

Skip to the conclusion if TL;DR What is an intuitive explanation for what a t-score gives you when computing confidence intervals? Background of my understanding of confidence intervals I just ...
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1answer
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Is it statistically valid to compare error measures for different sized samples?

I have forecasts for different sized samples using a variety of methods like DES (Double Exponential Smoothing), SES, MA and WA (Weighted Average) to test the strength of the forecasting models. The ...
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How to calculate standard deviation of 2D points along an arbitrary axis?

I have a data set $\vec P$ which consists of two arrays of coordinates $X$ and $Y$. I can calculate $\sigma X$ and $\sigma Y$, and derive the standard deviation of the vector lengths by $\sqrt{\sigma ...
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What measurement of error should I use to compare predicted model results to actual measurements (and why)?

Lets say I have a time-series dataset of measurements g that varies with time t and I also have a time-series dataset of predictions of these measurements (lets call this g1) that again varies with ...
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What is the difference between Noise, error and residuals?

I was reading about Kalman filter. http://web.mit.edu/kirtley/kirtley/binlustuff/literature/control/Kalman%20filter.pdf They talk about additive noise and error. I need to understand difference ...
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335 views

Why is cross validation error high upon overfitting?

http://www.cs.cornell.edu/courses/cs4780/2015fa/web/lecturenotes/lecturenote13.html ref: Figure 1: overfitting and underfitting Shouldn't cross validation error follow training error and remain low ?...
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57 views

Errorbar determination for non gaussian distribution

Suppose I have a data set which has a nice Gaussian distribution f(x), then I can "summarize" as Mean{f(x)} +- Std{f(x)} Where std stands for standard deviation. However, If my data does not look ...
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56 views

In which scenarios are the in-sample error and training error NOT the same?

In Elements of Statistical Learning, Chapter 7 (pages 228-229), the authors define the optimism of the training error rate as: $$ op\equiv Err_{in}-\overline{err} $$ With the training error $\...
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26 views

What are elliptical errors?

When can we have elliptical errors in linear regression?
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53 views

What causes a regression model to have positive error when output is large and negative error when output is small? [duplicate]

I have been playing with the Kaggle House Prices dataset for sometime. I have been using only the non-categorical features. After fitting LASSO I plotted the residual error vs true value scatter plot....
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Evaluating quality of predicted distributions

I have a set of data points $X_i, y_i$ where $x$ are the independent variables and I believe each $y_i$ can be modeled as being drawn from a exponential distributions with parameters $\lambda_i$. If ...
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Calculating Standard Deviation and Mean of N experiments of the same phenomena

I am a beginner in statistics. I want to calculate the mean and standard deviation of an entire time series data. Let's say I am measuring some phenomena y vs time t. I repeat the experiment say 3 ...
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Pattern of out-of-sample reconstruction error in NMF cross-validation: why is it monotonically decreasing? [duplicate]

I am using nonnegative matrix factorization, NMF (in its variant OPNMF, which is subject to additional orthogonality and $H = W^TV$ constraints) to factorize a dataset. To find the optimal number of ...