# 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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### Quantile regression for a sample of city sizes

I would like to estimate the following regression: $$\ln(Rank) = \alpha + \beta \ln(Population)$$ For an ordered sample of city sizes (from biggest to smallest), where $Rank$ is 1 for the biggest 2 ...
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### How to figure out what part of the data cause lad regression not be reach a unique solution?

wget -qO- https://i.stack.imgur.com/AQGsm.gif | tail -c +43 Using the above data (the plot of the data is shown below), I got the following error. ...
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### quantile surface of a mulitvariate distribution made of multiplication of marginal distributions assuming independence

How to perform quantile regression in a more elegant fashion? As discussed above, quantSheets() can only deal with one explanatory variable for computing quantile ...
29 views

### Best approach to Quantile Vector Autoregression

So I have a system of endogenous variables in panel form (24 Stock over 52 weeks). I would like to use quantile regression of one variable (Trading Volume) upon another (Social Media Sentiment). The ...
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### How to perform quantile regression in a more elegant fashion?

https://www.r-bloggers.com/2019/01/quantile-regression-in-r-2/ I see the above method. The regression result is a straight line. But the quantile of the real data may not be on a straight line. The ...
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### How many points fall below quantile regression-line?

I am sorry for the relatively easy question regarding quantile regression. I am a little stuck, and reading these resources I can't resolve this problem right now: (1) http://www.econ.uiuc.edu/~roger/...
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### Extract slopes for all fitted quantile regression models with different tau-values, R

I wonder how I can get the slopes of all the models that were fitted when I do the following: library(quantreq) z =rq(mpg ~ wt, data=mtcars, tau=-1) Putting the <...
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### quantile regression result different from Mann-Whitney U test

The results of the quantile regression and Mann-Whitney U test are very different. My sample size is 39. The quantile regression returns p-value of 0.83, while Mann-Whitney U test gives 0.33. Why are ...
67 views

### (rqpd) How to obtain the confidence intervals of a quantile regression model on panel data?

I had to adjust a quantile regression model on panel data and I used the rqdp package, however, when I needed the confidence intervals, I realized that the package does not provide the item in ...
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### How to obtain a 0 intercept in quantile regression

Quantile regression models are a type of models that provide estimates of the quantiles of a response variable $y$ given a set of covariates $X$ in the form of a linear equation such as  y = \beta_0 ...
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### How does ordinal regression compare to quantile regression?

I am familiar with ordinal regression and quantile regression at a high level, but would like a deeper understanding of the two beginning on how they differ. Can someone compare and contrast the two, ...
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### How to get main effects (deviance table) on the censored quantile regression in R quantreg::crq?

I know it's about R, but it's anyway a statistical question. I want to calculate confidence intervals for the survival quantiles (median and the 1st quartile). I was asked to use namely the censored ...
55 views

### Quantile regression on a constant: is this different from unconditional quantile?

With a linear model, estimating an OLS regression of y on a constant only will give us the mean of y. I was wondering whether ...
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### Is it possible to specify different quantile regression models for each quantile?

As the title says. I have never seen it, but I see no point that would prohibit me to do it. For example, a different set of variables might bear predictive value for the 25th-percentile of the ...
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### Hyperparameter tuning of quantile gradient boosting regression and linear quantile regression

I have am using Sklearns GradientBoostingRegressor for quantile regression as wells as a linear neural network implemented in Keras. I do however not know how to find the hyperparameters. For the ...
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### Hyperparameter tuning of statsmodels quantile regression

I am working in statsmodels and I am trying to do linear quantile regression with the function QuantReg. I can however not figure out a way to tune any ...
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### Hyperparameter tuning of gradient boosting and neural network quantile regression

I have am using Sklearns GradientBoostingRegressor for quantile regression as wells as a nonlinear neural network implemented in Keras. I do however not know how to find the hyperparameters. For the ...
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### Granger causality testing with rq() quantile regression

I am trying to test for Granger causality in my quantile regression. I have x (=position data) and y (=price data) in a dataframe called dat and then employ ...
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### Summation of median and quantiles of multiple forecasted variables

Assume that I have Y1_hat with its P10_1 and P90_1 and Y2_hat with its P10_2 and P90_2. Is it valid to sum Y1_hat and Y2_hat, sum P10_1 and P10_2, and sum P90_1 and P90_2? and would that present any ...
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### Quantile regression with an exponential function

The following equation: y = a*x**b where y is a nonlinear function of x. By taking logs, the equation can be expressed as: ln(y) = ln(a) + bln(x). I would like to run a quantile regression instead of ...
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### Interpretation of the coefficients from quantile regression with dummy independent variables only

I have a data set with only categorical variables, some are nominal and some are ordinal, but I assume there will be non-linear relationship between output and order of ordinal variables, so I have ...
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### How to detect endogeinity, in a quantile regression?

I ran a quantile regression on Stata. I strongly suspect that endogeneity is present. As one of my variables signs is inverted, in a result that makes absolutely no sense. But how do I move from ...
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### estimation in linear models: loss functions and response variables

Consider a dataset of $N$ iid samples $\{(y_i,x_i)\}_{i=1}^N$ drawn from a joint distribution $(Y, X)$ where $x_i\in\mathbb{R}^p$ and $y_i\in\mathbb{R}$. In this setting, it is my understanding that a ...
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### Which tests should be perfomed after quantile regressions have been estimated?

I´m performing a quantile regression. Initially I opted for a linear regression, but as I suspected that variations in X had different effects on the outcome variable across the distribution, I ...
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### How to understand the coefficients from regression at different quantiles. Do they correlated with each other?

I applied quantile regression on this example data: t<- data.frame(id=seq(1,100), measureX =rnorm(100,0,1),measureY = rnorm(100,0,2)) This is the code I used: <...
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### consistent estimation of quantiles (without overlapping quantiles)

I would like to forecast quantile ranges. The observations are assumed to be heteroscedastic. Mostly, I am confronted with the problem that quantile regression results for different quantiles do ...
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### Quantile interpretation

If I have have the score for $q=0.9$, say $Y=y_{0.9}$. Does this mean that the probability of measuring a score $<y_{0.9}$ is 0.9? Edit: Basically I have one dependent variable, $y$ (a type of ...
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### Quantile Regression Median place within bounds

In quantile regression I understand that I am estimating prediction intervals with an upper and lower quantile and that the .5 is supposed to be the median. However I have encountered a situation ...
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### Bias in Quantile Regression

What are the assumption for the quantile regression estimator to be unbiased? I looked up Koenker 2005 but only found a theorem on consistency.
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### Multivariate quantile regression group lasso in R

I'm trying to fit a multivariate sparse quantile regression model with group lasso. The regression is multivariate as there are several dependent variables, $Y=(y_1,\dots,y_k)$. The selected $X$s must ...
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### Presence of autocorrelation and estimation of coefficients [duplicate]

I am a beginner in quantile regression, quantreg package in R.I found that it is a good method to analyze data with outliers or non-normally disturbing data, but can´t find anything about ...
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### Testing equality of quantile regression slopes at different quantiles

How do I test if the quantile regression slopes are equal for different quantiles? E.g. I run a quantile regression at 5% quantile, 50% quantile (median) and 95% quantile and obtain the slope ...
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### How to interpret output of quantile regression with interaction terms?

I'm running a quantile regression on SPSS to examine changes in the income structure over time in a certain profession, specifically trying to see if there is an increasing income inequality by ...
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### Monte-Carlo Simulation for Quantile Regression

I am trying to perform a Monte-Carlo simulation using R. Currently I am getting stuck simulating the data. In a usual regression setting I would draw a random sample of the independent data and then ...
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### r quantreg - quantile regression with clustered standard errors

I fit a quantile regression using quantreg:::rq on clustered data. I use the Huber sandwich estimator to obtain cluster-corrected standard errors, which is ...
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### Heteroskedasticity-Robust Standard Errors in Median Regressions

Does anyone know how to compute heteroskedasticity-robust standard errors in median regressions in R? Assume the following example: ...
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### quantile regression parameter for desired confidence interval

I want to plot C% confidence intervals for a regressor (GradientBoosting in my case). I found this example on scikit-learn documentation https://scikit-learn.org/stable/auto_examples/ensemble/...
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### Quantile regression: confidence values for extreme tau

I need to examine extreme values in a distribution $y \sim N(\mu,\sigma)$. Since there are $i$ groups for which I want to look at extreme values, I consider using quantile regression. For simulated ...
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### How to model zero-inflated continous (from negative to positive) data

We have a dataset of around 20k observations. The dependent variable is the change (i.e. delta) on the amount of a common resource (e.g. land) of individual households in a year, so: It has negative ...
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### Is minimizing Koenker-Bassett error the only optimization problem that gives sample quantile? [duplicate]

Sample quantile can be estimated by solving $\min_\theta \sum_{x \in X}f_\alpha(x-\theta)$ $f_\alpha = \alpha |x|$ when $x>0$, $f_\alpha = (1-\alpha) |x|$ when $x\leq0$. Sample expectile can be ...
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### If we add a constant weight vector with an absolute function, does it still remain convex then?

We know that absolute functions are convex. Now what if we add a constant weight vector to it, does it still remain convex? Say the equation is Absolute loss regression + L1 regularization, we know ...
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### Why is no one using Deep Quantile Regression as alternative to MDNs?

There are numerous articles and implementations of Mixture Density Networks, however I have seen almost no literature in regards to using Quantile Regression with Deep Learning. Why is this the case? ...
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### Do values of predicted percentiles never decrease for higher percentiles in quantile regression?

I would like to please ask for your help concerning the following issue. After consecutively running two separate quantile regressions for percentiles $p_i$ and $p_j$ with $j>i$ [e.g., for the ...
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### Calculating the quantile of random forest test cases

I want to calculate the quantile of the observed value of a test case with respect to the prediction interval generated from a random forest, so for each test case I want the proportion of the ...
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### R package: Quantile regression with multiple group fixed effects and clustered standard error for more than 1 million data points [closed]

Could you please suggest R package for quantile regression that can include group fixed effects and clustered standard error for more than 1 million data points? I am afraid that ...
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### Control Variate Estimator for Quantile Regression

I want to understand how a control variate estimator for quantile regression is computed. Therefore I read Ma and Koenker (2006). I'am unsure if I understood every step to achieve the CV (control ...
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### Compute the inverse of a conditional quantile regression output

Brunello et al (2009) show that extended compulsory schooling leads to increased wages respectivly to the individual gender. Their empirical model first uses quantile regression to show the impact of ...
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### rq() delivers the same coefficient results for all tau

I created a large module (52 covariates mostly factors), to estimate the effect of compulsory schooling on log_earnings. I used the quantile regresion technique. Since I do my study in R I go with a ...