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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Plot ARIMAX model with confidence interval in R
I fit an ARIMAX model on the data here (this is annual copepod phenology influenced by seasonality of water temperature).
Here is my model formula:
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How can I best evaluate whether uncertainties (confidence/credible) are of appropriately width, in simulations?
I would like to evaluate how well two experimental designs perform with the goal of parameter estimation. I'm generating 1000 simulated datasets for each design and fitting the same model to all of ...
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Doubling your accuracy - extension
Frederick Mosteller's 50 Challenging Problems in Probability has a nice question I have not seen before, and I was wondering whether it could be extended.
49. Doubling your accuracy
An unbiased ...
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Bounding the error when using L1 regularization
I'm reading some lecture notes on High-Dimensional Statistics (https://arxiv.org/abs/2310.19244) and on page 59 I'm not able to follow the proof.
The setup is this: we assume that data in the form of ...
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How do I check if my measured values fit the manufacterer claim of "3m/3σ"?
So, let's say I have 10 values with the following spread:
$\text{standard deviation} = 2.5\text{ m}$
In order to check if 2.5m is valid for the claim 3m/3σ, do I calculate:
$3m/3σ = 1m/1σ$ (So a ...
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Is the sample MSE an unbiased estimator of any quantity?
We assume that there is a true function $f$ such that $y_i = f(x_i) + \varepsilon_i$. In any general regression setting, a common measure of the quality of the estimated true function, $\hat{f}$, is ...
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Test set imputation
Suppose that I have missing values in one of my features, and there are missing values both in the train and test sets. I want to impute using the median of the observed features. Should I:
A) ...
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What is the difference between $\epsilon$ and $Var(\epsilon)$?
I am beginning to read an Introduction to Statistical Learning (ISL). I'm reading the beginning of Chapter 2 Statistical Learning and I am confused on the difference between $\epsilon$ and $Var(\...
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How to explain correlation of error term of Bivariate Probit model from GJRM package
I am estimating a Bivariate probit model using the GJRM package. From the model summary - theta = 0.897(0.886,0.908), tau = 0.709(0.694,0.724). I am looking into ways how to answer the correlation of ...
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Taking the weighted mean of data points which have their own confidence intervals?
I am working with some data containing estimates for different areas and their respective populations. The creators of the dataset first surveyed each location and used Monte Carlo simulation to ...
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Condition Number for solving a linear problem using the normal equations or OLS
I've checked this post where it is asked about the condition number for OLS as well.
However, my question is more direct and conceptual, and less numerical. When reading the first pages of the paper ...
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How to quantify the systematic error in linear regression fit?
When performing a linear regression on a dataset $(x_i,y_i)$ of size $N$, using the linear model $y(x)=β_0+β_1 x$, the covariance matrix of the estimated coefficients, intercept $\hat{β}_0$ and slope $...
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Why is the log additive model considered more accurate than other models in parameter estimation using the maxium likelihood
I am trying to get a better grasp of the theory of parameter estimation using different error models used in Phoenix NLME. The log additive model seems to perform better for my use case and I am ...
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Relationship between Gini impurity and misclassification error
I understand the differences between Gini Impurity and misclassification error, but I am curious if the following result that deals with the relationship between the two is true:
Assume we have two ...
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