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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Non-asymptotic estimation error bound of quantile regression

If we have $w_j$ observations $y_i^j$ at points $\vec{x}_j$, $j=1,\cdots,N$, we can conduct quantile regression to get $$ y = \vec{k} \cdot \vec{x} $$ and use $$\vec{k} \cdot \vec{x}_0$$ to predict ...
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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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28 views

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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2answers
104 views

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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1answer
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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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95 views

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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45 views

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 ...
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Some questions regarding the conditional quantile regressions of Brunello et al (2009)

I want to replicate the study of Brunello et al (2009) using only the data of SHARE. The main idea of the paper, as I understood, is to show wheter aditional years of compulsory schooling have an ...
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124 views

Quantile regression vs probability density estimation

If you want to predict a range for a regression problem using a deep network, you can do quantile regression and go with (for example) 5% and 95% quantiles. The other option is predicting a ...
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redundant level dummy variable [closed]

In classical statistical regression analysis (e.g. linear regression) one level of the categorical variable is usually not used to create a dummy variable to create a reference (e.g. there is only one ...
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26 views

monotonicity constraint question

I used this model: quantile regression neural network successfully in a couple of project. I am now faced with requiring monotonic decreasing rather than monotonic non-decreasing behaviour. Could I ...
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1answer
181 views

quantile regression (cross validation in R) [closed]

How can I do a cross validation for quantile regression in R or any other methods to compare between multiple regression and quantile regression?
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Is there a joint test of model coefficients, effectively testing for main and interaction effects in quantile linear mixed model?

I am just reading this paper: Linear Quantile Mixed Models: The lqmm Packagefor Laplace Quantile Regression. Let us assume I have a repeated observation experiment, where I want to assess the effect ...
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1answer
507 views

How Do I Build a Quantile Regression Model with GradientBoostingRegressor from sklearn?

I am building a quantile regression model using scikit-learn's GradientBoostingRegressor algorithm. I was going to use GridSearchCV for hyperparameter optimization. Two questions: Does it make sense ...
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Is there a way to analyse main effects on quantile mixed-effect regression in the spirit of the “ANOVA” procedure (now for medians)?

I would like to analyse my data using quantile regression with random effect. The problem is I have also categorical covariates, which will "split" the output into corresponding levels. I ...
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1answer
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Modeling Expected Value Using Quantile Regression as an Ensemble

I'm trying to find a primer on a topic that I'm sure must have been studied, but I can't find anything on. Suppose we'd like to do regression in a supervised learning setting to learn the expected ...
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138 views

Quantile regression for panel data - what is a tolerable zero tolerance in `rqpd`?

I'm using the R package rqpd to perform quantile regression on panel data with penalized fixed effects and running into singularity issues. The issue can be "fixed" by simply decreasing the <...
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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 ...
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107 views

Singular Design matrix error for a weighted quantile regression from quantreg R

My question is related to the question from this thread (Cause of singularity in matrix for quantile regression). But I am not able to solve my specific issue. My data-set includes 2000 observations (...
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1answer
91 views

MAE regression gives biased regression parameters for symmetric error?

Consider a linear model, $$ y_i = \beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i. $$ From the Gauss-Markov theorem, I know that, under nice conditions, the $\hat{\beta}_{OLS}=(X^TX)^{-1}X^Ty$ ...
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Koenker & Machado (1999) goodness-of-fit criterion (R1)

Has anyone come across a journal paper or a book providing a rule of thumb regarding what R1 is appropriate in research that focuses on the impact of macroeconomic or bank-specific variables on bank ...
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92 views

Unconditional Quantile Regressions – interpretation

I'm using the contributions by Firpo et al. (2009) for my research on determinants of inequality and particularly the effects of cash transfers on income inequality. With a continuous covariate the ...
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26 views

Global Estimates for Quantile Regression

Quantile regression (QR) provides information at each quantile of interest (e.g., .1, .2 ... .8, .9), but to compare QR results with those from an ordinary least squares regression, you'd need to ...
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Using quantile regression results to select and weight variables for models

Linear regression is commonly used to identify predictor(s) (e.g., scores on cognitive ability or personality assessments) of job performance. Typically, predictors that exhibit a significant ...
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38 views

Formal method to predict probability of a continuous variable

I am trying build a regression to model cdf, i.e to predict the probability that a continuous variable exceeds an arbitrary threshold. I explored using quantile regression, but it seems that I have ...
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134 views

Power calculation for outcome tested using quantile regression

I am looking to power a study where the primary outcome will be tested using quantile regression (median time). Does anyone have any advice on how to power this & determine the sample size? In ...
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1answer
245 views

How to compute custom contrasts for linear quantile mixed model from lqmm

I would like to get custom pairwise contrasts and Holm adjustment for a linear quantile mixed model generated using the lqmm and glht functions, but my attempt generates an error. For comparison, I ...
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Why are the intercept values of my QR non-monotonic?

I was led to believe that when conducting quantile regression you would expect intercept values to increase as you go up quantiles. However, I have run a quantile regression and the intercepts are as ...

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