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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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Combining information from different quantiles

I have a number of "mostly" Gaussian distributions (in truth a Gauss core and longer tails). I am interested in the width of this distributions. Given that I do not know the amount of tails ...
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Obtaining z-scores for coefficients of quantile regression with sampling weights applied in R

I would need to obtain z-scores for coefficients of quantile regression with sampling weights applied in R to be able to compare results from different datasets. Can I just compute them as "z-...
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Quantile regression with sampling weights in R

I am trying to implement quantile regression with sampling weights in R for my analysis. I know in lm() and glm() in R, standard ...
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Median regression

I am trying to understand the reason I'm having different results estimating median values with R median and rq (quantreg) ...
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Asymptotic results for quantile regression uniformly over all quantiles

In the standard quantile regression (QR) framework, we typically consider only one quantile level of interest, say $\tau$. By standard asymptotic results, we obtain the asymptotic normality of $\sqrt{...
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Quantile Regression Detrending

Assume I have a time series, as the black one below. As shown, the quantile regression for 5%, 25%, 50%, 75%, and 95% quantiles show different slopes (in red). Even if not quite visible, the ratio ...
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Necessary diagnostics of multiple quantile regression

I am wondering what are necessary statistics for multiple quantile regression model. I am considering creating a model e.g. using the quantreg R package: ...
Mikołaj's user avatar
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Analysis of interactions in quantile regression models

I possess a large dataset with n ~10,000. My goal is to develop a quantile regression model using rq() from the ...
Mikołaj's user avatar
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Bootstrapping moderately extreme quantile regression

Let $(Y_1, X_1), \dots, (Y_n, X_n)$ be iid sequence drawn from $F$. For a fixed $q\in (0,1)$, consider the linear q-quantile regression $Q_Y(q|x) = \beta_qx$, where $Q_Y(\cdot\mid x)$ is the ...
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In R, differences in coefficients between single-level and mixed-effect quantile regression

I am using the lqmm package in R to estimate a mixed-effect quantile regression for the first time in an analysis of clustered data (individuals clustered within care providers). I am struggling to ...
Sam Wilding's user avatar
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Does multivariable quantile regression model with mixed effects require fractional polynomials for independent variables?

Hello Cross Validated community, I am currently working on a project involving a multivariable quantile regression model with mixed effects, where the objective is to explore the relationships between ...
Mikołaj's user avatar
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Gradient boosting and quantile regression performance issues [closed]

My goal is to develop a ML model that predicts the remaining flight time. To do so I have different features: distance altitude speed vertical rate Here is a plot showing the actual remaining time ...
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Modification of square loss analogous to absolute and vs pinball loss: what is elicited?

Quantile regression at quantile $\tau$ minimizes the following "pinball" loss function, $L_{\tau}$, and elicits conditional quantile $\tau$. $$ l_{\tau}(y_i, \hat y_i) = \begin{cases} \...
Dave's user avatar
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How do quantile time series forecasts work?

My office leadership is interested adopting “quantile time series forecasting”, the idea is query the model to predict the 5th, 25th, 50th, 75th and 95th percentiles of an RV given features such as ...
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Expectile loss to reduce dependent variables overestimation

Say I have a a bunch of covariates $X$, and a dependent variable $y$, where $y$ is collected from people. However, I know from psychology that people will tend to overestimate $y$ given $X$ in some ...
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Is my intuition behind the weight matrix correct for quantile regression?

Motivating Question I was asked by a colleague today why one would run a quantile regression on quantiles that are "extreme" (such as $.10$, $.90$, etc.), if there are too few observations ...
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The statistical power decreases as the time point change in the data increases [closed]

Let $X_1,\dots,X_n$ the data generated by the signal plus noise model having a change in mean at $\tau\in\Pi=[t_1,1-t_1],\;0<t_1<1$, which defined by: $$\begin{cases} X_t=\rho_0+\varepsilon_t,\;...
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What sense does adjusted $R^2$ and deviance explained mean for quantile generalized additive models (QGAMs)?

I've done some reading here in the past, and my basic assumption is that for a generalized additive model (GAM) or a quantile regression (QR), the following is generally true: For a Gaussian ...
Shawn Hemelstrand's user avatar
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Recentered influence function and OLS interpretation

I am working with Recentered Influence Functions (RIF) to estimate regressions in distribution. We have the following regression $RIF(F_y, \nu (F_y)) = \beta_0 + \beta_1X + \varepsilon$ where $\nu(F_y)...
Valentina Andrade's user avatar
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242 views

Implementing Quantile Loss function

I have been reading about Quantile Regression and the Quantile Loss function, but I have to admit I am a bit lost as how to practically implement it. I would like to use it to calculate the prediction ...
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What does it mean to have symmetric quantiles?

I'm using quantile regression for my paper, and my results are symmetric i don't understand what that means. Please explain the symmetry of quantiles and how does this effect the results and how to ...
Helpplease's user avatar
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Estimating quantiles using quantile regression

I understand that quantile regression estimates the conditional quantile of some measured variable (call the variable $y$), but can you use quantile regression to estimate an unconditional quantile of ...
John Smith's user avatar
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408 views

Quantile regression and sample size for a given tau

I am performing the quantile regression in R on a non linear model (that is done by using nlrq). I am getting the coefficients for the desired quantiles (tau = 0.05, 0.50, 0.95). All very nice, but ...
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For What Kinds Of Problems is Quantile Regression Useful?

I am trying to learn more about Quantile Regression. As I understand, Quantile Regression is used to estimate the conditional quantile of a response variable (given predictor variables). ...
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Use linear mixed model or linear quantile mixed model for non-normal residuals?

I started with this initial model: m1 <- lmer(response ~ treatment + (1|subjectID), data = data) However, the residuals of the model are heavy-tailed (presumably enough to violate the normality ...
Jade's user avatar
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Can I use multiple quantile regression to estimate the probability a dependant variable is above / below a certain value?

Let's say I have a dataset of characteristics of newly launched products in a retail environment, and the dependant variable Y is total $ sales in the first year of ...
SCool's user avatar
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151 views

Quantile Regression -- special considerations for time series?

I'm working on analyzing some hydrological time series/discharge data (for context, I don't have that extensive of a background in statistics or with time series). Essentially, the data is daily ...
abby23's user avatar
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Low coverage of prediction intervals from quantile regression using LightGBM on heldout data

I fit three models using LightGBM with quantile objective (which uses pinball loss) using alpha values 0.10, 0.50, and 0.90. The following code is used to wrap the three models into a single class. ...
Julia Maddalena's user avatar
1 vote
1 answer
181 views

Maximum likelihood and residuals for quantile regression

If you assume a Gaussian distribution for the "errors" of your regression model, you can express the maximum likelihood, so the coefficients giving the highest likelihood for the observed ...
FaresDjerourou's user avatar
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62 views

Cointegration in quantile regression

I used quantile regression for my research. My variables were significant but my pseudo r was low. So I tested for cointegration. All my variables are I(1) and when I run the models with raw (...
Helpplease's user avatar
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Can i add dummy variables before testing the residuals for normality?

I am using eviews 13 and I want to run these equations Co c yd yd(-1) Co c yd co(-1) With quantile regression I want to test the residuals for normality and ...
Helpplease's user avatar
3 votes
1 answer
51 views

Is it legit to use a point estimate along with a conformal predictive interval from a quantile regressor?

I have a quantile regression model that gives me prediction intervals (PI), and I also need to have a point estimate for all sorts of reasons (or at least something as close to a point estimate in a ...
cremebrulee's user avatar
3 votes
0 answers
80 views

Intercept in Quantile Regression

We all know that for the OLS model, if you center both $X$ and $Y$, the estimated intercept would be 0. I was curious if we can do a similar thing for Quantile Regression. Would it be possible if we ...
momo's user avatar
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187 views

Why don't quantile regression curves (qgam / mgcv) fit the probabilities optimally?

I'd like to model the optimal quantile regression curves of probabilities as function of xa, using qgam ideally (mgcv-based R package), but not necessarily: Data: ...
denis's user avatar
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Quantile regression visualization and evaluation

I'm trying to perform quantile regression in R on a multivariate data set, where I want to visualize the 10% and 90% bounds. I also intend to calculate PICP - Prediction interval coverage probability ...
OLGJ's user avatar
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Quality assessment of 2 quantile regression methods

1. Context I have a dataset structured like this: ...
Recology's user avatar
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72 views

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 ...
jdotes's user avatar
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275 views

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 ...
maarvd's user avatar
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1 vote
1 answer
154 views

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 ...
user12899748's user avatar
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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 ...
iYOA's user avatar
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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 ...
Levi M's user avatar
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12 votes
3 answers
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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 ...
Ggjj11's user avatar
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1 vote
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127 views

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 ...
A.F.R.S2022's user avatar
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1 answer
113 views

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 ...
Recology's user avatar
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666 views

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 ...
Sourabh Sharma's user avatar
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28 views

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 ...
user671269's user avatar
1 vote
1 answer
252 views

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 ...
Him's user avatar
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1 vote
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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) ...
shenflow's user avatar
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2 votes
1 answer
154 views

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 ...
Levi M's user avatar
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4 votes
1 answer
409 views

Estimating a quantile from an unknown distribution

I have a variable $x \sim N(0,1)$, of dimension $p$, with each $x_i$ independent. I want to find the quantile, $q$, such that $$\mathbb{P}\left(\frac{\sum_{i=1}^p (|x_i| - b_i) }{c} \geq q \right) = a,...
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