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-linear least absolute deviation regression with multiple global minima

I am fitting a single exponential decay formula with three parameters (a,b,c): y ~ $a \exp(-xb) + c$ using the LAD cost function: $ \min \sum |(y - f(x))| $. $x$ is in units of time (as is $b$), and ...
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15 views

How to forecast with quantile regressoin

If you have three quantile regression models with taus of 0.25, 0.5 and 0.75 and their coefficients how do you use these models to forecast a set of data not used to calculate the coefficients. In ...
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25 views

Different models for different quantile functions possible?

My aim is to estimate the 2.5%- and 97.5%-quantile function (to get reference intervals) for a specific score in dependence of age separated by classes of a third variable cag. So first I built 11 ...
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1answer
61 views

Errors in fitting a censored quantile regression model

I have an outcome with right censoring like this: ...
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37 views

Cross validating quantile regression

I applied quantile regression on some data and did it for tau = 0.25, 0.5, 0.75. After i got the estimates of each model, i did some cross validation on my hold out data. When i used the estimates for ...
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1answer
11 views

Uncertainty analysis

Here is my situation. I am trying to predict the 'entire' distribution of the dependent variable, not just the mean( or conditional mean). Does it then make sense to seprateley predict quantiles of ...
2
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1answer
39 views

Regarding the quantile regression via optimization approach

The quantile regression is defined through the optimization approach. But I am not clear how does the function of $\rho_{\tau}(u)$ related to the $\tau$-th quantile. Or in other words, how to derive ...
3
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1answer
48 views

Coefficient standard error of zero in quantile regression

I'm currently experimenting with quantile regression of a strongly right skewed outcome variable y on a 3-category exposure x (values 1,2,3). I wanted to model the .2, .5, and .8 quantile, using the ...
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31 views

Quantile regression cross validation

In a previous question i asked how to calculate the quantiles of my data so that i can do cross validation on a hold out set of data for my quantile regression model. But i think i understood what i ...
2
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1answer
60 views

Quantile regression forecast accuracy

I am doing a quantile regression in R with some data and then i want to test the accuracy of the coefficients on a another data set (hold out set). But i am not sure how to go about measuring the ...
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47 views

Comparing results from linear quantile regression with mean regression

Say we fitted quantile regression models with a set of quantiles between 0 and 1 and a linear regression (i.e. mean regression) to a same dataset with the same set of covariates. In terms of the ...
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512 views

Literature on IV quantile regression

In the last months I have read intensively about quantile regression in preparation for my master thesis this summer. Specifically I have read most of Roger Koenker's 2005 book on the topic. Now I ...
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22 views

Nonparametric Time Series Forecasting

I am trying to understand how Kernel Density Estimation (KDE) or (nonparametric) Quantile Regression can be used to forecast values given historical observations. For example, consider the following ...
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107 views

Predicted values for fixed effect quantile regression

I'm currently working with the method proposed by Koenker (2004) and Lamarche(2010) on fixed effects for quantile regression, for this I'm using the RQPD code in R. I would like to get the predicted ...
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16 views

Directional Derivative of a function containing an Indicator function - Optimiality condition for quantile regressors

I'm trying to understand a passage in Koenker's Quantile regression book (p.33). It says: (note that y,x, are vectors and w is the direction vector) With the first part of the outcome no problem: I ...
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1answer
94 views

OLS vs. quantile regression

I ran OLS regression in Stata. Based only on the results I got in OLS, is there any way to know if the quantile regression will be a better choice?
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1answer
38 views

What can be inferred when multivariable ordinary least squares and quantile (median) regression yield differing results?

There lies information in a discrepancy of the (unconditional) mean and median. For example, if the median is larger than the mean, the distribution must be left-skewed. Does this kind of inference ...
6
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1answer
98 views

Quantile regression estimator formula

I have seen two different representations of the quantile regression estimator which are $$Q(\beta_{q}) = \sum^{n}_{i:y_{i}\geq x'_{i}\beta} q\mid y_i - x'_i \beta_q \mid + \sum^{n}_{i:y_{i}< ...
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0answers
47 views

Figuring out quantiles in quantile regression

Suppose I have a dataset $\{y_i,x_i\}$ $i=1,2,...n$. For the response variable, $y_i$ as per quantile regression I have the following likelihood: $$p(y_i|\beta,\alpha_i,\sigma) ...
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1answer
31 views

Applying ensemble learning to quantile regression?

Is it desirable / possible to apply ensemble learning methods (boosting, bagging, etc) to the quantile regression problem?
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83 views

Quantile regression power analysis

New to the site and to stats here! This may be a silly question, but I haven't been able to find a satisfactory answer on the procedure for a power analysis (or general guidelines about sample size) ...
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237 views

What is the difference between conditional and unconditional quantile regression?

The conditional quantile regression estimator by Koenker and Basset (1978) for the $\tau^{th}$ quantile is defined as $$\widehat{\beta}_{QR} = \min_{b} \sum^{n}_{i=1} \rho_\tau (y_i - X'_i b_\tau)$$ ...
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1answer
97 views

Huber sandwich estimator in quantile regression

I need the description of Huber sandwich estimate method for quantile regression. I found this "a Huber sandwich estimate using a local estimate of the sparsity function". Sparsity function looks ...
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40 views

Mean of residuals in quantile regression are significantly differ from 0

Is it necessary to have mean of residuals which is equal to 0 in Quantile regression?
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199 views

Quantile regression vs. Li's regression: which should I use, and when?

Is there a general rule of thumb about when robust regression or quantile regression is preferred in the presence of outliers? For example, I have a dataset where the DV exhibits extreme positive ...
2
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1answer
279 views

Goodness of fit tests for quantile regression in R

What goodness of fit tests are usually used for quantile regression? Ideally I need something similar to F-test in linear regression, but something like AIC in logistic regression will suite as well. ...
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1answer
117 views

Quantile Regression - Interpretation of a significant quantile

I want to perform a quantile regression on two continuous variables; Y (DV) and X (IV). I want to find out if there is an significant association between Y and X. When doing this in R like: fit2 ...
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46 views

Interpretation of quantile regression when high quantile estimates are lower

Suppose I estimate a multivariable quantile regression $Q_Y(\tau | X) = \alpha(\tau) + \beta(\tau)X + \epsilon(\tau)$. Note that $X$ is a vector of independent variables. Suppose I then 'plug in' my ...
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140 views

Using quantile regression to predict probability of surpassing threshold

Consider a continuous response $Y$ and design matrix vector $\mathbf{X}$. These are related through some function $f(X) = Y$. Suppose that I am interested in estimating the probability that $Y \leq ...
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1answer
110 views

Linear Hypothesis for a quantile regression in r

I would like to test a linear hypothesis in a median regression model similar to example below. ...
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1answer
278 views

Quantile regression

I have a question regarding quantile regression. Supposing that I have 10000 observations with one response variable and several predictor variables in a dataset collected each year over several ...
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181 views

Random effect quantile regression repeated subjects in SAS

I want to run a random effect quantile regression with repeated subjects. The subjects bid on two different steaks and I have demographics as explanatory variables. Can this be done in SAS?
4
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1answer
140 views

When does quantile regression produce biased coefficients (if ever)?

It is easy to show using matrix algebra when least squares will produce bias. \begin{equation} \begin{split} \text{E}[B]& = \text{E}[(X'X)^{-1}]\times\text{E}[X'Y] \\ & = ...
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124 views

Simulation about quantile regression

This is what I have done in R: ...
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285 views

Weights in quantile regression for complex survey in R

I want to include sample weights to my quantile regression model, but I'm not sure how to do this. I've already define my weight, which are replicated weights already given in survey dataset ...
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1answer
160 views

Quantile regression with Stata

Is there a way to test the equality of quantile regression coefficients in one go using Stata? For example can I do the comparison of the coefficients of the 10th, 25th, 50th, 75th and the 90th ...
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363 views

Ways to find a confidence interval for robust and quantile regressions

I'm trying to compare a few regression models for my data. For linear regression everything is quite understandable, but robust and quantile regressions are not so obvious. I could not find almost ...
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143 views

Evaluate Quantile Regression results and t-stats at different levels

I have a few questions regarding quantile regression and how to interpret the results. I have several independent variables and I want to figure out which combination of variables have the highest ...
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73 views

Quantile regression standard error and the OLS standard error

I was asked by a non-statistician what is the driving factor for the standard error estimates of the parameters. Here are my thoughts: From asymptotic theory, both OLS standard error and Quantile ...
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49 views

Calulating a mean coefficient effect based on quantile regression estimates

I have used quantile regression to estimate a particular coefficient for the 10th, 20th, ... 90th percentiles. Now, I want to estimate the mean effect of the coefficient across the whole ...
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1answer
260 views

Model performance in quantile modelling

I am using quantile regression (for example via gbm or quantreg in R) - not focusing on the median but instead an upper quantile ...
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1answer
104 views

Quantile regression with one predictor

Is there any closed formula for quantile regression with only one predictor? Motivation I need to implement in SQL median regression with one predictor. It is quite easy to implement OLS with one ...
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1answer
745 views

What are the assumptions for quantile regression?

What assumptions must be fulfilled in quantile regression?
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1k views

Quantile regression: Which standard errors?

The summary.rq function from the quantreg vignette provides a multitude of choices for standard error estimates of quantile regression coefficients. What are the ...
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112 views

Quantile regression analyzing the conditional quantiles of one of the regressors?

Given response $Y_t$ and predictor $X_t$, we can use OLS to analyze the conditional mean; $E[Y_t | X]$. Quantile regression can be used to analyze the conditional quantile function; $Q(Y_t(\tau)|X)$. ...
5
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1answer
461 views

What are the red lines in quantile regression plot (quantreg package)?

Using plot.rq in the quantreg package in R, we can plot the coefficient estimate distribution, and get something like this: ...
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2answers
265 views

Quantile regression and heteroscedasticity/autocorrelation

I hear it said [1] that QR makes no distribution assumptions about its error term. Question 1: Does this mean that heteroscedastic and serially correlated disturbances do not effect the ...
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1answer
205 views

Quantile regression with dummy variable that's equal to 0 over most $t$

I have the model $Y_t = a + b*X_t + c*D_t + e_t$, where $t \in T = \{1,...,3000\}$ and $D_t$ is a binary variable equal to $0$ over $T \backslash \{20,21,...,30\}$, and equal to $1$ over ...
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3answers
860 views

When is quantile regression worse than OLS?

Apart from some unique circumstances where we absolutely must understand the conditional mean relationship, what are the situations where a researcher should pick OLS over Quantile Regression? I ...
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125 views

(Quantile regression) AR(1) variable in the design matrix

I'm not doing a pure QAR (quantile auto regression) but I do have a lagged dependent variable (AR(1)) as a predictor. I'm using the quantreg package in ...