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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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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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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local linear quantile regression using R

I am supposed to follow the paper of Yu and Jones (1998) for nonparametric estimation of conditional quantile functions. It is in particular the local linear model which they called "local linear ...
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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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64 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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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 ...
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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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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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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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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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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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78 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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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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148 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 ...
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171 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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87 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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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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111 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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89 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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226 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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142 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?
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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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Simulate from quantile regression [duplicate]

Does the smooth relationship given by quantile regression produce unreliable results, particularly at the extremes of the data range? The hint I have got is that this question will be explored by ...
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Simulation about quantile regression

This is what I have done in R: ...
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187 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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144 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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242 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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How to calculate the weighted sum of absolute deviations to determine AIC for quantile regression

I would like to know if there is a way to calculate the sum of the weighted absolute deviations for quantile regressions with package quantreg? I'm following the ...
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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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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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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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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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544 views

What are the assumptions for quantile regression?

What assumptions must be fulfilled in quantile regression?
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864 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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107 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; $Q(Y_t(\tau)|X)$. ...
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327 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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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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176 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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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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(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 ...
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(Quantile regression) Which standard error for heteroscedasticity & serial correlation

I have heteroscedastic and autocorrelated residuals in my multivariate quantile regression model. What's the quantile regression standard error estimator that's robust to this? Something hopefully ...
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Presenting the error term in a quantile regression specification

Let $Y_i$ be the response and $X_i$ be the independent variables. Whenever I've seen a quantile regression specification they'll go: $Q_{\tau}(Y_i | X_i) = a(\tau) + b(\tau) X_i$ Or, alternatively: ...
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Optimizing regression coefficients to predict the largest outcomes

What is a sound methodology to improve the efficiency of the regression coefficients when we are interested in predicting the larger values of the marginal distribution (tails)? For example, we want ...
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Explaining quantile regression to nonstatisticians

I recently submitted a paper, in which I used quantile regression, to a psychology journal. Although I thought I had already put enough thought in a clear exposition of quantile regression, the ...
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Logistic quantile regression – how to best convey the results

In a previous post I’ve wondered how to deal with EQ-5D scores. Recently I stumbled upon logistic quantile regression suggested by Bottai and McKeown that introduces an elegant way to deal with ...
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570 views

Quantile regression prediction

I am interested in using quantile regression for some of my models, but would like to have some clarifications on what can I achieve using this methodology. I understand I can obtain a more robust ...
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What diagnostic plots exists for quantile regression?

Following on my question for OLS, I wonder: what diagnostic plots exists for quantile regression? (and are there R implementation of them?) A quick google search already came up with the worm plot ...
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About interpretation of the results of quantile regression

After applying quantile regression with t=0.5,0.6 on the data set WBC( Wisconsin Breast Cancer)with 678 observations and 9 independent variables($inp_1,inp_2,...inp_9$) and 1 dependent variable(op) I ...