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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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Derivation of Formula for linear regression with data points forming a circle

Suppose we have one dimensional data with following conditions.1. The value of this single feature lies in the closed interval [-a,a].2. The associated target value with each data also lies in the ...
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Calculating the margin of error on an estimated total number of class instances in population

I have a completely random sample of size 10 from a population of objects (population size 1000, if that helps) which can belong to either one of two classes, A or B. Based on a guess from superficial ...
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Estimating the true error rate from the optimistic resubstitution (or apparent) error rate of a PLS-DA model

In short, I'm trying to calculate the 'Upper bound 3' [Ref, p.4] of the true error rate for my partial least squares regression model (PLS-DA), separating two classes A and B of a sample set. Let me ...
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High error value when estimating model parameters

I have a non linear system of ODEs and to estimate 4 of the model parameters I am using Matlab fmincon by minimising the sum of squared errors (SSE). I have only 5 ...
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1answer
25 views

How to improve a model that is consistently underestimating

I've been trying to predict house prices (real data from my country) and I noticed that initially, errors are centered around zero, but around the $2,500,000 mark, the model starts underestimating ...
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46 views

Base Error Rate

I am working for my final exam and I saw this sample question: Given this dataset, Assume we have the following gender detection problem, given the observed hair length and height (both discrete ...
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Independence and identical distribution of the error observations [duplicate]

if I know that the observation (xi,yi) are i.i.d. this should not imply that the r.v. are independent, indeed there could be some correlation between the same vector of observation i.. so could I ...
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1answer
56 views

calculating overall error in k-fold cross validation

when using k-fold cross validation i thought the overall error was equal to the mean of errors of each fold. the error being anything from MAE and RMSE to NDCG,F-measure, precision and recall. however ...
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Is the error term a sum of r.v.?

`If in a econometric model I have: $y = \beta x + u$ where u is the error term, we have: $u = y - \beta x$ Supposing that $\beta=1$, $y\sim N(0,1)$, $x \sim N(0,1)$ and $x$, $y$ are independent. ...
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Accounting for errors in independent variable through Gaussian process regression

In Gaussian process regression (GPR), one applies a kernel (i.e. covariance function) to describe the similarity between observed and predicted data in the domain. The diagonal of the covariance ...
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Stationary and ergodic r.v: relation between error and independent variable

In time series often hold the condition that a r.v. is stationary and ergodic, allowing the application of the law of large number. If in a model as: Y= a + bX + u ...
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Independence relation between observation and error [duplicate]

Having a simple model like: Y = a + bX + u where u represent the error term, if I know that the observation of X and Y are i.i.d, also the error term is i.i.d?
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criteria for percent error?

I have 2 arrays. The first array is system rating {69.73, 56.93, 68.64, 65.58, 70.36, 67.44, 56.34, 75.03, 51.58, 65.7} The second array is human rating ...
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1answer
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Propagation of asymmetric uncertainties

I have two (fully independent) measurements of the same quantity X. Each of them reports a measurement $X_{\sigma_L}^{\sigma_R}$ where $\sigma_L$ and $\sigma_R$ are the left and right uncertainties (...
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36 views

weighted kappa for intra/inter-rater reliability in SPSS

I am working with ordinal scales for cerebral atrophy (ratings 0 to 4) and vascular burden (ratings 0 to 3) assessed by two raters. I have installed the extension bundle for weighted kappa from SPSS ...
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1answer
31 views

Is error function always assumed and convex?

While updating weights of the neural network, most of the algorithms use convex optimisation because of the reason that error is a convex function. My doubt is that whether the convex-ness of error ...
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1answer
42 views

Why errors are written additively in a regression model?

I was curious about: Why do we write errors (or disturbance term) $\varepsilon$ as a additive term in a regression model? To elaborate, whether we consider a paramteric or non-paramteric regression ...
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Type II error for share price event study - what is the difference between one and several securities?

I have a question regarding the type II error for a specific event study. It is a case study (i.e. one observation) with daily share prices. I want to test whether event day abnormal returns are ...
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Error variance estimation with weights

I am using data which include a (sample-)weight for each observation, i.e. the data is from a survey that has weights to make the sample representative for the US-population. I perform OLS to get some ...
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16 views

Correct approach to Mean Absolute Percentage Error

Currently I've been working on sales data. I have different categories that have very different figures (e.g. Groceries vs Technology), so I decided the best approach was the MAPE. The thing is, I ...
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14 views

Calculate the Confidence Interval for the Error of Model

I am not sure I am thinking about my problem the right way, so I am looking for the right approach. I have a data set that, for the sake of argument, has a mean of 1 and a standard deviation of $\...
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1answer
118 views

How to use optim function in R on my custom Residual Sum of Squares function?

I'm trying to use the optim function in R to find the optimal values for $\alpha$ and $l_0$ for my custom residual sum of squares (RSS) function, but the values I'm ...
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1answer
40 views

Margin of Error question from a stats amateur

Our organisation is currently putting together a report based on a salary survey of employees within a specific industry (a huge array of questions with varying types of answer). We surveyed 11,000 ...
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1answer
25 views

Better to Minimize Absolute Error or Sum of Squared Error?

I have an Excel model which predicts the number of customers for a given month. The prediction depends on a churn rate. I have the absolute error (actual vs predicted), along with squared error and ...
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Are there any lower bounds on generalization error?

There are multifarious generalization error upper bounds in terms of VC dimension , uniform stability and Rademacher complexity and recent work in terms of mutual information and total variational ...
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58 views

Using full covariance matrix of a linear fit reduces the errors?

I am currently studying linear fitting and error propagation. The model to fit is this: $$B ( N , Z ) = a _ { v } A - a _ { s } A ^ { 2 / 3 } - a _ { c } \frac { Z ( Z - 1 ) } { A ^ { 1 / 3 } } - a ...
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What is prediction in PRF exactly? (Regression Question Series - Part 5)

Preface: This is slightly alternate question from previous question here. It arose because I find difficulty grasping the basics of regression still (sure, I am doing multiple revisits to basics again ...
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Is there a relationship between the “significance level” of a KS test and the size of the error bars in a given data set?

Suppose I have a data set with error, $\mathbf{d}+\mathbf{\Delta d}$ where the error is some percentage of the data (e.g. $\mathbf{\Delta d} = \epsilon \mathbf{d}$, $0 < \epsilon < 1$). I also ...
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Why error sum of squares has n-2 df (possibly not duplicate, please read on)? (Regression Question Series - Part 4)

In simple linear regression, the error sum of squares is given by $$ \text{SSE} = \sum_{i=1}^n(y_i - \hat{y_i})^2 \\ \hat{\sigma}^2 = s^2 = \dfrac{\text{SSE}}{n-2} $$ where $n-2$ is the degrees of ...
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29 views

Calculation of RMSEC (Calibration Error), Which data should be used?

I got a bit confused about RMSEC. I got how RMSECV and RMSEP are calculated and their meaning, though. I am working based on 2 papers which summarize their results with RMSEC, RMSECV1, RMSECV2 and ...
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1answer
23 views

What goodness-of-fit tests avoids the ambiguity in chi-square statistic?

The chi-square statistic is a fairly standard goodness-of-fit test defined as: $$\chi^2 = \sum_k^N \left ( \frac{d_k-m_k}{\Delta d_k}\right )^2$$ where $\mathbf{d}$ is a vector of data with error $\...
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Characterizing estimator, estimate and RV (Regression Question Series - Part 3)

Given a sample set $(X,Y)$, supposing $X$ is fixed and known, Population Regression Function,PRF: Hypothesizing the underlying population, we have, $$\begin{aligned} & E(Y) = \beta_0 + \...
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Moving average, MA(q) model, why we use errors in regression?

Could you please explain(dummy friendly) why we regress past errors in moving average(MA(q)) model?
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Is residual in a SRF, an estimate of error in PRF? (Regression Question Series - Part 2)

PRF: Given a sample set $(X,Y)$ we hypothesize underlying population has a regression line as follows. \begin{aligned} & E(Y) = \beta_0 + \beta_1x & \scriptsize \text{(1) PRF} \\ &...
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which control chart can use for error variance/

I have a series of error variances from the model With what type of univariate shewhart control chartI can control monitor error $variance(\sigma^2)$?
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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 other words, ...
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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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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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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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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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75 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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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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2answers
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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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1answer
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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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1answer
54 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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1answer
74 views

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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20 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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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 ...