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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14 views

Alternatives to predictions' MSE that are 'proportional' to $Y$

Assume that all values are real. let $Y$ be a vector of observations and $\hat{Y}$ be a vector of predictions. Then the MSE of the predictions is $$1/n\sum_{i=1}^n(\hat{Y}_i-Y_i)^2$$ Let $$S = ...
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17 views

Frog leap experiment

We have a frog that finds itself on a complex graph. The vertices are labeled by integer indices, and the objective is to compute the probability for the frog being able to save itself, which ...
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4 views

R lmer error: Model is not identifiable. Error in base::chol2inv(x, …) : 'a' must be a numeric matrix [on hold]

I'm very new to using R, and I've been trying to perform some ANOVA analyses using both lsmeans and difflsmeans via lmer. The code that I'm using was given to me by someone who knows what they're ...
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9 views

Planned Orthogonal Comparison Type I Error Rate and the Number of Independent Contrasts

I am confused about Type I error rate and the number of planned independent contrasts in Planned Orthogonal Comparisons in one-way ANOVA. If we have a factor with 5 groups and we would like to test ...
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16 views

Using a change detection error matrix approach for raster aggregation

I am assessing annual land use change along a 10 year period and have rasterized a vector land use dataset to base resolution 'n' metres to do so (vector data is taken as ground truth, errors in it ...
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1answer
32 views

Error term in multiple regression model

I am trying to run a multiple regression model to see the effect of field characteristics such as soil texture, slope and hydraulic conductivity on drainage density. My samples are agricultural ...
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18 views

Modeling error in regression

A few weeks ago I posted in this forum about a regression analysis I wanted to run. My outcome was number of organs and they values went from 1-7. Well, as someone pointed out, I could have some bias. ...
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22 views

Estimator of true probability — understanding margin of error for very small probability

I have a coin whose probability of landing on heads when flipped is unknown, but could be anywhere between 0 and 100%. I want to flip the coin some number of times and estimate the true probability ...
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6 views

Gini impurity and generalization error

Has anyone seen papers on relationship between information-based criterions (such as Gini impurity, information gain etc.) and generalization error? Is there theoretical justification of using such ...
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29 views

Forecast accuracy metric for forecasts over different time horizons

I a dataset of 81 oil price forecasts from more than 30 different forecasters. Those forecasts consist of a forecast made on various days in 2014 for the average oil spot price of 2015. For instance, ...
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1answer
14 views

How can I deal with numerical errors in a large-scale linear regression?

I am currently conducting a linear regression on a large-scale data set which has many sparse features ($\simeq 10^5$) and many observations ($\simeq 10^6$) by using scikit-learn. (Most of the ...
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1answer
31 views

Prediction interval, forecast error for a function of a forecast

I have two variables $X$ and $Y$. For each variable I created a forecasting model (using time series) and estimated $X_{t+1}$ and $Y_{t+1}$ and the prediction interval and the error for each. I have ...
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9 views

Error propagation taylor second-order (multivariate)

I'm trying to understand how the second-order approximation mentioned in this posting http://stats.stackexchange.com/a/13005 looks like for a mulitvariate function. I have only found the ...
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13 views

k.means relation between sum squared error and variance

I work with k-means algorithm and I don't understand the relation between sum squared error and variance. Is there a relation between these values?. I work with k=1. And the values are Sum squared ...
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1answer
21 views

calculate the internally studentized residual

it says that ...an ordinary residual divided by an estimate of its standard deviation $s(e_{i})$ As we can see from the example that mean for four residuals is 0, so ...
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25 views

Log transformed MAE to original value

In order to evaluate the forecast accuracy of a model I'm using a step wise cross validation to get a MAE value and use that again to calculate the MASE. As part of the model specification the data ...
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1answer
22 views

Compare RMSE between original and logged time series data

I have some time series data, both in the original form y and in logged form log(y). I should compare the models generated by applying neural networks and find the best one. How to decide which one is ...
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4 views

Interpolating data with errors (limited model knowledge)

I have data which I know follows a function $y = f(x)$ such that it is quadratic i.e. $y =\alpha x^2$ for some $\alpha$ when $x\rightarrow 0$ and $y = \beta x$ for large $x$. The data itself has ...
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1answer
32 views

Derivation of Equation of Reducible and Irreducible Error [duplicate]

I am currently reading An Introduction to Statistical Learning by James, Witten, Hastie, and Tibshirani, and I am stuck on one of the leaps they take when defining reducible and irreducible error. ...
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26 views

Alternating Least Squares Test Error better than Train

I have been running some trials for recommendations using Collaborative Filtering, specifically Alternating Least Squares (ALS). I am using two versions of ALS, one with fixed lambda regularisation ...
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1answer
15 views

How may I convert Perplexity to F Measure

In the practice of Machine Learning accuracy of some models are determined by perplexity, (like LDA), while many of them (Naive Bayes, HMM,etc..) by F Measure. I like to evaluate all the models with ...
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11 views

Can I propagate standard deviation and standard error together?

Can I mix standard deviation and standard error when propagating error? For example, if I multiply two values and one has error in terms of standard deviation and the other in terms of standard ...
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8 views

Modelling errors of linear & logistic regression

How can the errors of linear regression models be modelled to make the results even more accurate? Also, how are errors in logistic regression measured? Is it possible to model the errors of logistic ...
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30 views

How to compare posterior distributions for different observed data? KL-divergence?

So I'm solving an inverse problem with the Bayesian approach $p(u | y) \propto p(y| u )p(u)$. Assuming I have two datasets $y_1$ and $y_2$, what can be said about the difference in the posteriors ...
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1answer
17 views

What method for forecasting error measuring in a poisson process?

There's so much different measures for the forecast error that I kind of lose the sight on which one to use. Out of the following: MAPE, ...
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1answer
10 views

Size of Mean Squared Error (MSE)

Is there a rule or a scale for judging if a certain MSE is small, very small, big or very big? Please give also a source to underpin your recommendation.
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18 views

Are linear regression errors independent? Mean independent? Uncorrelated?

All I know is that we assume zero conditional mean (and hence zero mean) and conditional homoscedasticity (and hence homoscedasticity). When trying to prove that $E[(\hat{\beta_1} - \beta_1)\bar{u}] ...
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10 views

Expectation of Error 2k squares?

There is a regression model $$Y_n= X_n \beta + \epsilon_n $$ where, $X_n$ is a $n \times p_n $ matrix, E($\epsilon_n$) = 0, and Var($\epsilon_n$) = $\sigma^2$ How can I figure out E( ...
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1answer
34 views

What to check in cross-validation - MAE or MSE?

When using cross-validation for model selection, should one look at MSE or MAE. I know that MSE and MAE are related but which is the more appropriate measure?
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1answer
21 views

ANOVA / t-test to compare the errors of different models

I have two forecasting models, moving average and single exponential smoothing. The values of Mean Absolute Percentage Error (MAPE) is 5.2%, 5.8%. Since the difference of MAPE between the models are ...
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19 views

How to use the off-diagonal terms of the covariance matrix when calculating confidence intervals?

The nonlinear fitting routine I use is MATLAB's fitnlm and it gives the covariance matrix. How can I take into account the off-diagonal values of this matrix to ...
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1answer
31 views

Difference between errors and residuals. What is the mean and variance of each of them?

Suppose there is a simple linear model $y=\beta_0+\beta_1x+u$. Can we state that $\bar y=\beta_0+\beta_1 \bar x + \bar u$? I have this question because I come up with $Var(\bar u)$ when doing some ...
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13 views

Effect of number of samples on error in classification/regression

Let's say for a classifier, $E_{out}$ is the test error and $E_{in}$ is the training error, $N_{out}$ is the no. of test samples and $N_{in}$ is the number of training samples. I want to know the ...
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27 views

Understanding Mean Squared Error

When determining the quality of an estimator, I understand a simple metric such as, if the expected and predicted are close, then we consider this instance to be correct. Then sum up all correct and ...
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18 views

Prediciton with a help of regression that minimizes the RMSE

I have two data sets containing the same variables (43 variables). The first set contains 107 observations and the second - 30. The dependent variable is "Revenue" (the values of this variable are ...
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1answer
26 views

T-test between groups while removing within group variability

I'm comparing two conditions based on an outcome variable of satisfaction with group learning (scale 1-9). The first condition consists of telling 3 groups of 3 people that their group project WILL be ...
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1answer
25 views

which model with count data and 3 factors, problem with glm

This is for a study for the abundance of counted individuals of the taxon Nematocera (gnats) in dependence of the three factors "Betrieb"(two levels), "Standort" (8 levels) and "Variante" (3 levels). ...
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10 views

Nonindependent Errors

I'm trying to better understand the way in which error can be nonindependent, specifically in terms of distinguishing between crossed/within vs. nested/between. That is, determining whether error ...
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16 views

Confidence interval for the median - continued

I have a set of values $x_i\quad i=1,…,N$ of which I can calculate the median M. Each $x_i$ has an error $\delta x_i$. The $x_i$ values are the result of a maximum likelyhood estimation and their ...
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23 views

How to calculate errors/confidence intervals of parameters from least squares fitting which have high correlation

I'm no statistician but I want to be more honest about my error bars. Let's say I have a dataset which is described by some model $f(x,{params})$ where ${params}$ is a vector of many parameters for ...
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10 views

How to sample for success/failure from small populations and probabilities

I am interested in sampling data that comes in a yes/no form. A couple things I would like help in understanding. Why does the reasonable sample size change when my population shrinks? We might be ...
2
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0answers
112 views

Regression models with comparable MAE but differing R²

I have trained two regression models on the same dataset. They perform with comparable mean absolut errors $MAE_{1,2} \approx 0.45$, but the coefficient of determination differs significantly with ...
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34 views

Help for understanding zero training error

I am working on an image classification problem. I have 750 training examples, each with 30000 features (the pixels). I use SVM with a linear kernel and 10-fold cross validation to train and valid the ...
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1answer
31 views

The conditional expectation of the error term in single index model

There is a statement in the "Non-parametric Economics" book chapter does not make sense to me. Here is the statement. A semi parametric single index model is of the form $$Y = ...
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2answers
46 views

Error of empirical probability for unfair die

I roll an unfair $256$-sided die $n$ times ($n > 1'000'000$) and count the rolled numbers in a histogram. I then calculate the empirical probabilities ${p_e}_i$ for $i=1, ..., 256$ by taking the ...
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1answer
26 views

GLM - Zero-Inflated distribution

I'm fitting a zero-inflated poisson model using the "pscl" package. The formula that I'm using is: ...
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7 views

Gaussian Mixture has lower error rates on larger set

I'm training a Gaussian Mixture Model to cluster satellite image features using the RGB values of each pixel and some subset of Haralick features (calculated from a 9x9 window around the pixel). The ...
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1answer
18 views

Calculate Forecast Error: Different ways using the mean?

Example: I've got an forecast with 2000 values. Let's say they are for one year. I can group my values into months. Every month can include a different number of single values. (JAN with 200 values + ...
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37 views

Longitudinal analysis with possible duplicates and missing data

Short version: When following patients that can be present in distinct databases, how does one estimate errors due to duplicates (patient present in two of the databases) or misclassification (due to ...
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19 views

Estimating Sailboat Wind Measurement Calibration Error

Sailboat performance is always judged relative to the wind. The optimal approach to sailing the boat is different in light wind than in heavy. So, knowing the wind helps by setting accurate ...