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### Is quantile regression a maximum likelihood method?

Quantile regression allows to estimate a conditional quantile for y (like e.g. the median of y,...) from data x. I do not see any distributional assumptions about y being made. This seems in contrast ...
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### Best loss function for nonlinear regression

I have some nonlinear nonnormal data that I am trying to analyze. The data has been normalized to -1 to 1 and detrended with polynomials of an order of 3. I'm trying to determine if there is a special ...
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### How to incentivise AI to make risky predictions

I'm trying to build a weather forecasting AI. I have a dataset that contains the peak temperatures for each day. I have trained it with MSE as the loss function and it has worked fairly well. I do ...
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### How to calculate pinball loss for quantiles and for point forecasts?

I have a few general questions about pinball loss: Is a pinball loss typically calculated for each point in the forecast horizon or is it calculated across all points in the forecast horizon? How is ...
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### How do quantile time series forecasts work?

My office leadership is interested adopting “quantile time series forecasting”, the idea is query the model to predict the 5th, 25th, 50th, 75th and 95th percentiles of an RV given features such as ...
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### Real-world example of quantile loss used for evaluation

We can use quantile loss (a.ka. tick or pinball loss) for training a model or for evaluating predictions. (It is helpful to distinguish the two clearly, e.g. as done here.) I am interested in the ...
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### Oversampling for Continuous Values

I am trying to predict the processing time of a process by using xgboost regression algorithm in python. However I realised that my samples data is skewed to left and my algorithm struggles to predict ...
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### Giving more importance to under prediction (mean absolute error) than over prediction for forecasting

Just curious to hear any thoughts on weighting over prediction in mean absolute error to minimize the penalty since I'm more interested in under prediction, if that makes sense. Basically, I'm ...
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### Which Forecast Evaluation Metric To Use?

It is a forecasting problem. I need an evaluation metric which penalizes under-predictions more than over-predictions. Also I want it's range in certain interval (say 0-100), so that it becomes easier ...
1 vote
Quantile regression at quantile $\tau$ minimizes the following "pinball" loss function, $L_{\tau}$, and elicits conditional quantile $\tau$.  l_{\tau}(y_i, \hat y_i) = \begin{cases} \...