12 questions linked to/from Quantile regression: Loss function
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### Using Leibniz integral rule when minimizing Expected Absolute Loss [duplicate]

Consider choosing $\theta^*$ that minimizes the expected absolute loss: \begin{align} \tag{1} \int_{\Theta}|\theta-\theta^*|\pi(\theta|\mathbf{x})d\theta= \int_{-\infty}^{\theta^*}(\theta^*-\theta)\...
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### How to find a value that ensures 70% of population is above it

i'm trying to solve this statistics problem. i have a certain number of samples that are randomly chosen to represent a population. (yellow dots in the picture) over those samples are run tests to ...
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### Examples of “risk-averse” loss functions

Could you give me some examples and/or references on "risk-averse" loss functions (i.e. penalizing the underestimates more then the overestimates)?
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### Appropriate error measure

Statistics is not realy my field of knowlegde but I am trying to find an answer for the following question: Many cities nowadays have a bike share system. Suppose you were asked to predict how many ...
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### Formula of quantile regression?

We already know that the estimator of quantile regression defined by LAD (Least Absolut Deviation), minimizes sigma |e_i|. But I also found a formula that minimize with an integral, not a sigma ...
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### Different error weighting for positive and negative residuals for OLS?

For OLS-estimators in multivariate regression analysis, it logically doesn't matter whether an error is positive or negative. I was wondering if in some situations it might make sense to weight a ...
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### Should we use the absolute value of errors in quantile regression loss function?

I am trying to use quantile regression loss function. Most of the implementations I see here, here, and here are using the error directly: ...
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### What does, actually, the quantile regression asseses, assuming single two-level categorical covariate, difference in medians or median of differenes?

I know that, for a single, two-level categorical covariate, like sex={Male, Female}, the linear regression coefficients are about difference in means. It's like the t test. Does the quantile ...