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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Should I sample or compute the innovation term in the recursive estimation OLS algorithm applied to time-series data?
I have time-series data $\{Z_{[t]}\} = Z_t, Z_{t-1}, ..., Z_1$ of length $L$, and I would like to estimate a model for the $\{Z_{[t]}\}$ so I can forecast $Z_{t+1}$ as a function of a number of its ...
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Root Mean Square Error of the addition of two measurements whose RMS Error is known
I am working on a measurement system which tries to measure the distance between two values i.e $\Delta F=F_1-F_2$. Where $F_1, F_2$ are the values I actually measure. I have set up a Monte Carlo ...
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How to construct forecast confidence interval from the historical RMSE?
I'm reading a FED paper on forecast uncertainty estimation. Here's the link
One of their methods to estimate forecast interval is illustrated in the following figure
According to the description: &...
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How should I interpret the assumption of the regression?
I read an econometrics book which states one of the basic assumptions of regression is that
$$E(u|x) = 0$$
In another book however I see it written that
$$E(u_i|x_i) = 0$$
Are these two saying the ...
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How to predict more than one future values in ARMA model
I want some help with predicting more than one future values in ARMA. I saw that the similar question has been asked here. But it is only helpful for predicting one future value.
For estimation of the ...
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Error propagation for arbitrary function with a very large number of variables
let's say I have some function, $f(\vec{x})$, whhere the input is a vector of very large size $\vec{x}=[x_1,x_2,x_3,...x_n]$. n is tens of millions, but let's say for now it's just very large. I can ...
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Can I say that the relative root mean squared error is the averaged percentage error?
RMSE is an error metric in which the mean of the data minimizes its loss function:
$\text{RMSE} = \sqrt{\frac{\sum_{t=1}^{n}(y_t - \hat{y_t})^2}{n}}$
But it gives ...
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If the error term in a regression is squared can it still be a linear regression?
So basically I’ve been taught that in a linear regression model the parameters alpha and beta cannot be squared when defining the equation of our model, does this also apply for the error term (...
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Error between average of averages and true average [closed]
It is known that the average of averages can yield an incorrect result as compared to the true average.
The classroom example comes to mind: if the test results of class A is [50, 60, 100], class B is ...
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Fit a curve with unknown function assuming normal errors [closed]
Let say that I have a 1D experimental dataset $y(x)$, which contains noise due to experimental error. Is it possible to estimate the data by assuming that the errors are normally distributed? (The ...
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How to convert standard error of the mean (SEM) into a percentage change
I have performed a t-test between groups, but I only have Mean, SEM, and N. Now I would like to look at the percentage change between these two groups, and compare this percentage change to another ...
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What error metrics to use for time series model with time-step ahead hyper-parameter?
Background
Denote the forecasted value by a Time Series ML Model as
\begin{align}
\hat{y}_{t+\tau} \, (t, \tau)
\end{align}
where $t$ is the current time-step, $\tau$ is the time-step ahead. The ...
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How to obtain the standard deviation of several data sets with multiple measurements within each set?
I have done an experiment and repeated the set of measurements 3 times, totalling 3 data sets.
In each set of measurements the machine acquired 30 data sets. Meaning that in total I have 90 data ...
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OOB in Random Forests - Detailed Calculation
In the book An introduction to statistical learning, it is mentioned that:
One can show
that on average, each bagged tree makes use of around two-thirds of the
observations. The remaining one-third ...
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Question regarding the assumption for Gaussian process regression error and Bayesian optimization
I am wondering in the research of Bayesian optimization and Gaussian process regression how the function error could be rigorously quantified. I am aware that in general either of the following ...
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Regression models with uncertainty as T-Distribution [duplicate]
Are there any distributions which represent uncertainty about $\hat y$ as a $t$ distribution.
In other words: $ p(y\mid x, ~\text{model}) \sim \mathbf T(\hat y, \text{df}, \sigma)$ where $\bf T$ is a ...
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Identify the best method in test data and use it in real data that might have different characteristics?
we are trying to identify the best method to measure X in our upcoming study.
We do not have any data from the same populations in the upcoming study but
we have some test data (input data and ground ...
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using the GARCH model, the result of 10 forecasting values are (erroneously) equal. Any suggestion?
I am currently facing a problem with my GARCH model, specifically with the forecasted results. It appears that all the forecasted values are turning out to be identical, which leads me to suspect that ...
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How can I compute the probability of committing a type 2 error?
Let $X_1,...X_n$ be an iid sample distributed as $\mathcal{N}(\mu,1)$. We have the following tests $$H_0: \mu=0~~~\text{vs.}~~~H_1:\mu\neq 0$$and we use the statistic $T=\frac{1}{n}\sum_{k=1}^n X_k$ ...
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Suggestions for resources about statistical analysis
I am wondering if anyone has suggestions for resources discussing how to properly carry out statistical analysis across multiple groups, for something like evaluating the accuracy of a thermometer ...
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Error in linear interpolation of $n$-dimensional curves
Let's assume we are given an $n$-dimensional smooth curve $\gamma:[a,b] \rightarrow \mathbb{R}^n$ and $N$- sampled points $\{x_1,...,x_N\}$ of that curve.
Now we use linear interpolation (or a higher ...
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How to calculate the error on the ratio of a counting experiment?
In an experiment I repeat some task $n$ times and count how often the task completes successfully. This gives the number $m$. Therefore the success ratio is
$$
r = \frac{m}{n}
$$
To calculate the ...
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The standard error of precision from the standard error of intermediate precision and repeatability of a analytical chemical method
A validation report of an analytical method (to determine the assay of a product) is given and the goal is to try to determinate the overall uncertainty of it. I started with calculating the standard ...
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How do I deal with many zero values in terms of correlation?
I am currently working on my master thesis. I have determined a simulation model for tax returns and to verify this I would like to use true values.
I would like to determine the correlation between ...
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Neural Network is always giving same result [duplicate]
I am trying to write the neural network as written in the book "Neural Networks and Deep Learning" by Michael Nielsen. I have finally gotten the code to run but every epoch results in the ...
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Using multiple individual regressions Y~X_i to find the best two combination of predictors
Problem Statement
Let's say I have multiple solved OLS regressions of the form $Y \sim X_1$, $Y \sim X_2$, ..., $Y \sim X_n$
I want to find which best two combined are the best predictors combined, ...
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How to represent 2 standard deviation values as one error
I am working out a percentage survival between 2 conditions (e.g. in the presence/absence of antibiotic). For both mean values I have a standard deviation. How do represent the error in the % survival ...
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Which loss function to use if entries in a prediction span multiple orders of magnitude?
I am modeling the rates of chemical reactions with a ML-model (specifically a neural network with a lowish number of parameters). However, the rates (or technically the formation rates), the ...
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RMSE of Training data is lower compared to test dataset
First of all, this is not a case of Overfitting.
The task is to forecast Temp using univariate Single Step forecasting.
I have trained the LSTM model with on jena climate dataset(Dataset https://...
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Relative error on a log-log plot
Since absolute error plotted on a log-log plot will result in asymmetric error bars, my understanding is that this would give a misleading view of the precision of a measurement. I can plot instead ...
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Top 2 box (T2B) margin of error calculation. Where's the mistake?
I have a survey asking customers to rate their satisfaction on 1-5 scale.
I'm interested in learning the margin of error for a derived quantity, namely the "top2box%", i.e. the percentage of ...
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How should I visualize errors that can be on either size of mean
I'm building an app to help players improve the accuracy of their shots in pool (pocket billiards). Someone might miss shots to either side of the centerline (overcut or undercut), and that's shown ...
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prediction error in GLM
Can you please explain why this statement holds?
a distribution where the variance is proportional to the mean will better tolerate larger prediction errors occurring with larger predictions than one ...
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Gam using mgcv is giving negative deviance explained
I run a null binomial generalized additive models (gam) using mgcv and it gives negative deviance explained!
As far as I know deviance explained is analogue of R^2 ...
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Mean Squared Error (MSE) formula for data points in higher dimensions
The form for MSE for $N$ data points with scalar values $Y=[Y_1,Y_2,...,Y_N]$ is given by the formula:
$$ MSE = \frac{1}{N} \sum_{i=1}^N (Y_i - \hat{Y}_i)^2 $$
How I see it, $ d_i = Y_i - \hat{Y}_i$, ...
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Is there an error metric that decreases the weight when the target is near zero?
As precipitation prediction models can only predict positive values, they won't be able to undershoot small values by much. When it comes to overshooting, there is no boundary. High precipitation ...
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Bound for $L_2$-error of random forest estimate
I am struggling to understand a certain inequality based on the regression $L_2$-error of a regression function estimate.
The setting is that of random forests for regression.
Let $\Theta = \{ \...
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Relative Error and Chi-Squared-Test
I have a histogram A that holds a distribution describing kinematics. Now I want to approximate that distribution by other distributions that were made under simplified assumptions. Then I want to ...
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How to compute sample variance and/or mean square error as a percentage?
Say I have a set of measurement values $y_\text{m} = (y_{\text{m},1}, \dots y_{\text{m},N}) $, and compare these with some ground truth $y = (y_1, \dots y_N)$. Then, if I understood correctly, I can ...
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How to propagate errors from two sources
Suppose I performed 10 measurements, and have the dataset:
...
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Derivation in integrating part of the expected prediction error (ESLR)
I have a doubt in the derivation expected predicted error in the Integration part. The link in given below, please refer.
Expected prediction error - derivation
\begin{align*}
EPE(f) &= \int [y - ...
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Non-linear regression: confidence intervals and root mean squared error
I ran a non-linear regression using scipy's curve_fit. I fitted the data using an exponential function $y=a \ e^{bx}$ and calculated the confidence intervals. This is what I get:
However, when I fit ...
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Evaluation metric which is able to handle cases where actual value is 0, different units and isn't disproportionately affected by outliers
Just as the title imply, I am searching for an error evaluation metric with the following characteristics:
able to handle cases where actual value is 0
can evaluate different units/scales
isn't ...
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Error propagation through multiple fitting
I have a collection of $N$ sets of data $(x_i, y_i)$ that I believe follow the model
$$
y_i = a x_i
$$
where $a(b)$ is a linear function of some parameter $b$ that is known for each $i$. My process is ...
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Quantifying the confidence that the most sampled outcome is the most probable outcome
Let us say we have a cheater's six-sided die, which we can assume to be unfair with an unknown probability distribution. We want to know the most likely roll with this die, and so we roll it $N \gg 6$ ...
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$\text{var}(\hat{u})\text { and }\text{var}(\hat{Y})$ derivation
Could anyone provide me with either the steps for derivation for these formulae or a textbook that covers these ols derivations?
The textbook i’m currently using does not go over this.
$$\text{var}(\...
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Margin of Error: Why doesn't this form require p?
This page has a margin of error calculator:
https://www.surveymonkey.com/mp/margin-of-error-calculator/
Below, it gives a detailed example. The example conforms to my understanding of MOE. However, ...
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a question about leverage and variance of the predictor variable [duplicate]
In a simple linear regression:
Assume that the leverage of a specific data point equals 1 (maximum leverage),
from my understanding, it also means that the variance of the estimated error (e) of that ...
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Combining Absolute and Relative Error
When using a machine-learning model to predict a quantity for different sub-populations of different sizes, I'd like to compare the error between sub-populations (e.g. future population per country ...
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How to find the linearity of 5 points
I am currently developing a software in C. I have an array (matrix) that contains some coordinate points like this (125 points for now):
\begin{bmatrix}x1&x2&x3&x4&x5&...&x125\\...
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