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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33 views

Quantile regression and linear regression coefficient comparison

I am trying to understand the concept of quantile regression by modelling the monthly expenditure on insurance on several variables. The R package ...
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31 views

How to check that quantile regression forests provide valid predictions?

I am using quantile regression forests to predict the distribution of a measure of performance in a medical context. I am using the ranger R package for that purpose. I would like to have advices ...
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What is the quantile covariance?

Suppose that $X$ is a p-dimensional random vector and $Y$ is a random scalar. Then, Dodge and Whittaker (2009) indicate that the covariance of these two variables can be formulated as a minimization ...
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1answer
159 views

How to find a value that ensures 70% of population is above it

i'm trying to solve this statistics problem. i have a certain number of samples that are randomly chosen to represent a population. (yellow dots in the picture) over those samples are run tests to ...
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18 views

Quantile regression ANOVA and ANCOVA [duplicate]

ANOVA posits that the mean of a particular group is equal to the overall mean plus some amount. If we find that amount to be significant, then we decide that the groups don't all have the same mean. ...
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Time series quantile regression

I have time series where at each time step I have a bunch of real-valued points (e.g. individual purchases on a given day), and would like to produce a forecast of several quantiles. One approach I'm ...
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32 views

which quantile select when doing quantile regression

I want to know how strongly a variable restricts the maximum values another variable can reach. I asume there will be some degree of error in my estimates of both variables. Also, the availability of ...
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1answer
118 views

Pooling across quantile regression analyses from multiple imputed datasets (quantreg, MICE)

We have a dataset looking at predictors of reading comprehension ability, with a few missing data points here and there. After lots of going round in circles I think that multiple imputation is the ...
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17 views

Is survival analysis is a time series models

I would like to apply a quantile regression model on lung cancer (survival). My question is, does survival analysis is a time series models. Or can I fit linear quantile regression models to this data?...
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Limitations of unconditional quantile regressions?

I've been reading that conditional quantile regression may yield results that are not interesting or generalizable in a policy context, and that unconditional quantile regressions (UQR) are a better ...
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17 views

How to compare two plots of two different quantile regression models

I am new to the quantile regression. I found an example Here that compare vine copula quantile regression model with a linear quantile regression model. The example provides the plots of the two ...
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46 views

Quality of a quantile regression learner

Given a learning algorithm that selects and trains quantile models, how do we evaluate it? One idea is to - use the algorithm to train a model on a synthetic dataset with labels drawn from an ...
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Quantile regression, minimizer [duplicate]

Let's consider values $z_1, \dots, z_m$ and the minimizer of the function: $$ \min_q (1-\tau) \sum_{z_i<q} (q-z_i) + \tau \sum_{z_i \geq q}(z_i -q)$$ Why does minimizing this function gives the $\...
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Dependent variables, regression

I am trying do make some descriptive statistic. In my dataset I have ID, Age, time from start of being registered, sex, birth-place. The time from start of being registered minus date 15 June 2019 ...
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25 views

Nonlinear quantile regression SSReg analogue

I have recently remembered that $SSTot = SSRes + SSReg$ fails to hold in the case of nonlinear regression. $$ y_i-\bar{y} = (y_i - \hat{y_i} + \hat{y_i} - \bar{y}) = (y_i - \hat{y_i}) + (\hat{y_i} - ...
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Is quantile regression a special case of OLS?

Quantile regression is often advertised as a way of "predicting change in the dependent variable that is not the mean." It seems like one can do this with linear regression, however. Am I correct? ...
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In quantile regression how do you use the equivariance property with many variables $Q_{h(x,\epsilon)|x}(u|x)$?

I have seen in a text book that if we assume monotonicity and independence then if $Q_{y|x}(u|x)$ is the conditional quantile function. and $Y=h(x,\epsilon)$ then $Q_{y|x}(u|x)= h(x,Q_{\epsilon|...
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What is the median of $y_{i}$ given $x_{i}$ for the function $y_i=\max\{0, x_{i}^{\prime}\beta + u_{i}\}$

$y_{i}$ is a kx1 matrix, $x_{i}$ is a kxk matrix, $\beta$ is a 1xk matrix of coefficients and $u_{i}$ is a kx1 matrix of error terms. $y_i=\max\{0, x_{i}^{\prime}\beta + u_{i}\}$ and $med(u_{i}|x_{i}...
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Error estimates for coefficients of a non-negative quantile regression

I am looking for a way to provide an error estimate for coefficients obtained from a non-negative quantile regression. The complicated part aside from positivity constraints is that my observations ...
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Quantile Regression loss function/ check function proof

Can anyone help me to show that this statement is true. I have looked in Koenker's Quantile Regression (2000) and a load of other sources but I cannot find a solution. There seems to be a trick ...
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How do I formulate logistic quantile regression models?

Which of these models is most appropriate given the data (prediction is my goal), and why? I haven't had much experience with quantile regression, and I have so far assumed (probably niavely) that ...
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How does quantile regression compare to logistic regression with the variable split at the quantile?

I googled a bit but didn't find anything on this. Suppose you do a quantile regression on the qth quantile of the dependent variable. Then you split the DV at the qth quantile and label the result ...
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Method to combine quantile regression forecasts

I am predicting electricity usage for customers which is highly skewed. Regular regression models did not fit well due to skewed distribution, hence I tried quantile regression. I'm obtaining the ...
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105 views

The use of the quantile regression

I would like your help regarding the quantile regression. I was wondering if it makes sense to use the quantile regression when the relation of the number of data between variable x and y is 1 to 1, ...
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1answer
97 views

Making a model to predict the error of another model

So basically I have a machine learning model where I want to have a prediction interval, the model is XGBoost so it is tricky to do Quantile Regression and I was looking for an alternative method to ...
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42 views

Interpret Intercept Plot from Series of Quantile Regressions in R

Essentially, I am looking at a set of housing data from 2000-2017 and I am examining 'affordability' by year through quantile regression. The Y variable (affordability) is a ratio of what an ...
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470 views

What are the advantages of linear regression over quantile regression?

The linear regression model makes a bunch of assumptions that quantile regression does not and, if the assumptions of linear regression are met, then my intuition (and some very limited experience) is ...
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1answer
29 views

Interaction term and sample selection

I have a dependent variable Y which is continuous. I want to study the impact of X on Y using OLS in a linear model, but I suspect the impact of X is more important for observations with a high value ...
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Should log-log relationship of relative std.err. vs. sample size always be linear?

I am seeing a strong linear relationship between log-log plot of number of samples vs std.error of the mean estimate. As far as I can tell, this is expected (e.g. link). Since std. error is calculated ...
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1answer
86 views

Evaluation metric for prediction interval?

In quantile regression (https://en.wikipedia.org/wiki/Quantile_regression), what are some suitable evaluation metrics? Intuitively, I think a good model should have: good accuracy, i.e. the ...
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139 views

determine quantile for prediction with quantile regression (forests)

Having a fitted quantile regression (forest) model is great. However, how does one choose the best quantile to perform the actual prediction? One idea would be to use bootstrapping. In other words, ...
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80 views

Fastest algorithm to solve quantile regression with single predictor and no intercept

I was wondering what would be the most efficient algorithm to solve quantile regression with a single predictor and no intercept? I tried a Brent line search, but unfortunately that's no faster than ...
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2-Stage Least Absolute Deviations (2SLAD) Estimator with Quantile Regression in R

I was reading a paper, in which they introduce the following analysis, but without much further explanation as to what is being done: Since our key variables of interest are endogenous, we follow ...
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31 views

Quantile regression line formulation

I want to apply a quantile regression model to my data, and of course would like to understand at least in principle what quantile regression does to my data. Now I understand the basic concept and I ...
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1answer
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Confidence Bands for Quantile Regression

Can anyone suggest a way to construct confidence bands on a particular quantile regression line? I am working with the quantreg package in R.
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576 views

Formulating quantile regression as Linear Programming problem?

How do I formulate quantile regression as a Linear Programming problem? When looking at the median quantile problem I know it is \begin{align} \text{minimize } & \sum_{i=1}^n |\beta_0 + X_i \...
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102 views

heteroskedasticity and quantile regression

I am working on a quantile regression. I saw that there are tests for heteroskedasticity like a test by machado and silva (MSS) and a KB test. However, i have also read that having errors with ...
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Derivatives of quantile loss function [duplicate]

I'm reading a text - Roger Koenker (2005) Quantile Regression [page 8] - that goes like this: Consider the function $$R(\xi) = \sum_{i=1}^n \rho_\tau(y_i-\xi)$$ where $$\rho_\tau(y_i-\xi) =(y_i-\xi)(\...
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86 views

partial dependence plot for quantile regression forest

I am using this code: ...
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Quantile-Regression and Grid-Search

i am currently experimenting with quantile-regression in h2o. I am building prediction intervals. For the individual regression models i am looking after R^2, RMSE and also quantile-loss. I performed ...
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1answer
117 views

SGD and quantile regression

It is my understanding that the quantile loss is not differentiable (at 0) so base gradient descent cannot be used. However, Vowpal Wabbit which is an SGD-based learner very much includes quantile ...
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56 views

using rstanarm for quantile regression

I understand that rstanarm can be used for GLMs, GAMs and hierarchical models. Does anyone know, if I can use it to estimate quantile regression models? If not, are there other Baysian R package, ...
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32 views

quantile regression and high cost of under-predicting

I have a regression problem where it is better to over-predict than under-predict (i.e. the cost of under-predicting is higher). I think the use of quantile regression with a tau above the median - e....
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1answer
272 views

How to you measure the accuracy of a model that gives quantile forecasts or distributions of forecasts?

I've come across some recent demand forecasting approaches that present methods where instead of generating just a point forecast, the model outputs a set of forecast quantiles, or a distribution of ...
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1answer
166 views

Similarity LAD and quantile regression

With Least Absolute Deviations (LAD) regression coefficients are estimated through minimization of the sum of the absolute values of the residuals. Quantile regression aims at estimating either the ...
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29 views

In multivariable quantile regression, how can we determine which observation corresponds with a particular quantile?

I'm trying to use quantile regression to solve an areal interpolation problem as described in this paper: https://www.tandfonline.com/doi/abs/10.1080/00045608.2011.627054 Basically I have a set of ...
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Quantile Regression - What is the “bandwith”?

I am trying to perform a Quantile Regression on hundreds of series. From time to time, I have very small series that issue a warning. Here's a sample code to reproduce : ...
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How does quantile regression behave when having more variables than observations?

When having a dataset with a larger number of variables than observations, it is not possible to build a linear regression model, because such a model would have an infinite number of possible ...
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1answer
539 views

difference-in-difference regression run as quantile regression

The usual regression equation used to estimate difference-in-difference is the following: y i t = β 0 + β 1 Treat + ...
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52 views

How to visualize the relation between the variance of y and the interaction of x and z

I want to show that the variance of a dependent variable y is a function of the interaction of two independent variables x and <...