# Questions tagged [quantile-regression]

Quantile regression allows us to estimate the effect of a set of predictor variables over the entire distribution of the outcome variable or any particular quantile.

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### Best method to construct reference curves

I need to construct reference curves (or percentile curves) for a continuous outcome variable, let's say Y, with the covariate age on the x-axis. The curves will also be made across different ...
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### eviews quantile panel data [closed]

I would like to set the quantile breakpoint for my dependent variable in the panel data in eviews. However, no matter how hard I try, it doesn't work. Can you help me to correct this code? ...
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### Quantile Regression and Independent Errors

I am struggling to understand two different quantile regression specifications and the assumptions of conditional quantile independence and full independence. In the first specification, suppose we ...
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### Prediction of mean in addition to quantiles using quantile regression in ranger

I am confused about the possibilities to predict the mean using quantile regression forests. In my understanding, quantile regression enables the prediction of the probability distribution, i.e. the ...
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### Can you do Quantile regression for probabilistic forecast with Gaussian process regression (GPR)?

I am learning probabilistic forecasting and there are three way to do it, quantile regression, prediction interval and probability density forecast. Can i perform quantile regression with Gaussian ...
1 vote
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### p-values unstable using quantreg::rq in R [closed]

Using R, I m performing a backtest on a time series by using quantile regression (quantreg::rq) on a number of features. These features are selected based on a condition such as p-values <= 5%. If ...
1 vote
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### How to generate quantile forecasts from first differences?

Let's say I have a time series and I am taking the first differences and training a model to output the predicted 95% quantiles of these first differences at future time horizons. If this was just a ...
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### quantile regression vs mannU (median difference)

I want to compare the medians of an interrupted time series, for example, years 2019-2020 with 2021-2022. The data is not normally distributed and the distribution of the data is not similar. Would ...
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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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### Add equality constraint and positive coefficients to quantile regression function in quantreg package in R

I want to fit a quantile regression to $y_t= \alpha+ \beta_1 x_1 + \beta_2 x_2 +\beta_3 x_3 + \beta_4 x_4 + \epsilon_t$ $\rightarrow$ (1) rq function can do the job for me however I want to add two ...
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### What type of data should I generate to observe/amplify a crossing problem in quantile regression?

1. Background Crossing problem in quantile regression can be observed when we want to estimate several conditional quantiles (e.g. τ = 0.1, 0.2, . . . , 0.9), as two or more estimated conditional ...
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### Does linear regression mean the model fit line has to be straight? [duplicate]

When we fit a linear reg model, do we get a straight line equation? So, it means there is no way we can get a curved line from it. Then why in some examples over internet we see curved line for linear ...
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### Slope estimates of the quantile regression

In the Quantile Regression model $$y_i=x_i^T\beta + \epsilon_i,\ i=1,2,....,n$$ when the error terms are iid then can we expect that the slope estimates for the conditional mean and quantiles to be ...
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### Estimates of the Quantile Regression

In the Quantile regresion model we assume that$$y_i=x_i^T\beta +\epsilon_i,\ i=1, 2, 3, ....,n$$ such that the conditional quantiles of the error terms are zero and for the OLS model we assume that ...
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### Robustness of Quantile Regression

Is the 99th Quantile Regression model a robust model? From my understanding, Quantile Regression is supposed to be robust in nature, but removing some outliers using IQR, the results obtained by 99th ...
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### Estimate Conditonal Moments from Conditonal Quantiles

In Chang et al. "The Higher Moments of Future Earnings" (2014), the authors say say that based on (predicted) conditonal quantiles of a variable $y$, one can derive the (predicted) ...
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### Quantile Regression and MannU test for median difference

I am looking to determine whether two medians are not equal and attempt to estimate the median difference between the two. From my research, I have found this can be done by performing the Wilcoxon ...
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### How to interpret the quadratic affect in the quantile regression for birth weight example

I have read a nice article about the quantile regression using the brith weight as one example. The article can be accessed via this link Here. The two figures in the second row in page 8 are ...
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### Predicting percentiles with percentile data [closed]

I have a few independent variables and 5 dependent(target) variables. The target variables are percentiles (10th, 25th, 50th, 75th, 90th) and I want to predict the same in that order. What approach ...
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### Loss function for conditional IQR: is it just the difference between $q_{0.75}$ and $q_{0.25}?$

Quantile regression lets us estimate the conditional first and third quantiles by using particular loss functions that I’ll call $L_{0.25}$ and $L_{0.75}$, respectively.  l_{\tau}(y_i, \hat y_i) = \...
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### Can a Variable Be Both Dependent and Independent?

We can see that the GDP growth, represented by "y" is the dependent variable and independent variable. I would like to perform quantile regression in Eviews, with ...
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### Scikit-learn QuantileRegressor memory allocation error. No issue with statsmodel QuantReg with the same data

I'm trying to fit a quantile regression model to my input data. I would like to use sklearn, but I am getting a memory allocation error when I try to fit the model. The same data with the statsmodels ...
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### What is the meaning of a quantile regression model that predicts the conditional mean?

What does that phrase "quantile regression model that predicts the conditional mean" mean? How to interpret that? I found it in Liu et al. (2020). The authors have compared the results of ...
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### Which metric to use to evaluate Quantile Regression?

I have a prediction problem for which I want to predict the 75% Quantile using Quantile Regression. I am a little bit confused on how to evaluate this model (and also compare different models). If I ...
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### Proof of $\left|c_{i}-c_{j}\right|\left\{\begin{matrix}\ge 2,{\rm of}\,3/4\,{\rm probability}\\<2,{\rm of}\,1/4\,{\rm probability}\end{matrix}\right.$

FA Premier League 2019/20. The season was affected by the COVID-19 Pandemic while each team had a so-called quarter of their schedule left. ("quarter" ? Since each team has 4/9 or 5/9 number ... 116 views

### Dependent value largely right skewed. What are my options?

I am modeling a dependent variable which is heavily right skewed by a large number of independant variables. This variable is integer. But let's assume this is our model. $Y = a_0 X_0 + a_1 X_1 + b_0$...
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### Using an independent variable correlated with the residuals in quantile regression

If an independent variable correlates with the residuals in quantile regression, does it produce biased coefficient estimates? In ordinary least squares regression, if the independent variable is ...
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### Time fixed effect - calculate the net of time effect

I have a data that includes two categories, one being Manchester and another Leeds. This is panel data. I have a Year variable, a dummy for city 0 (Man) 1 (Leeds) and a dummy for each Year. How would ...
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### n-th quantile for bivariate variable

I generate a 2000 bivariate random samples which are negative correlated. I used np.quantile to generate 10 quantile from this random samples. The related point is marked in the following figure. I am ...
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### Theory understanding behind quantile regression

As part of my studies in ecology, I am trying to reproduce a quantile regression method described in Karlsson et. al (2022) (source: https://arxiv.org/pdf/2202.02206.pdf) My starting point is this: ...
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### Variations in the output of quantile regression models

I am trying to implement quantile regression models with R for the first time (I am new to this regression approach). Here is the code that I am running: ...
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### How to interpret the quantile regression based on random forest?

I have read the Q&A how-are-the-results-of-multivariable-quantile-regression-interpreted and the recommended paper (Petscher and Logan, 2013). I have taken the Wine Quality Data Set, built the ...
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### How to calculate the correlation by the Spearman method for each quantile of the quantile regression in R?

I'm trying to calculate the Spearman's correlation coefficient for each quantile of my quantile regression (to later calculate the R² of each quantile), but the package I know of (QCSIS) uses Pearson'...
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### What are some methods for comparing 2 separate quantile regression curves?

I am currently working with a dataset using the QuantregGrowth package in RStudio to determine the 2.5th/97.5th percentile curves of a biomarker across the age spectrum. I have a pretty good handle on ...
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### OLS is BLUE (or BUE) to minimize MSE. Is quantile regression is BLUE to minimize MAE?

The Gauss-Markov theorem considers "best" as "lowest mean square error (MSE)" and a recent version of the theorem shows OLS is not only BLUE but also BUE: https://www.ssc.wisc.edu/~...
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