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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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13 views

Quantile Plot in RMS::orm [migrated]

I'm not sure if this question is more pertinent to CrossValidated or StackOverflow. I'm happy to migrate it if necessary. I'm trying to reproduce the plots from Roger Koenker's quantile regression ...
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Estimate distribution from mean and prediction intervals

I'm using an ML-model (gradient boosting) to predict mean, upper and lower quantiles of a target variable which is gamma distributed. I want to construct distributions for the predictions and figured ...
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Model to be used with only median data and weights

I am finding a decent method to demonstrate if there is trend in the median age at diagnosis of multiple cancers. I do not have a breakdown of individual ages though, all I have is only (1) Median age ...
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Quantile loss 50th is MAE, is it? [duplicate]

I'm not sure the above sentence is true, but I read it here, here and here that quantile loss function percentile 0.5 is MAE(mean absolute error), Is it true(Yes or No)? and How?
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For non-parametric regression which one has better interpretation and properties, GAM or quantile regression?

As in the topic. I want to interpret data for which I have no clues about the distribution. It's neither count, percentage, continuous. I don't want any transformations. Instead I would like to ...
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Efficiency of OLS versus Quantile regression estimator

If I have a linear model $ y_i = x_i'\boldsymbol\beta + \epsilon_i $ and I assume that OLS estimator of $\boldsymbol\beta$ is unbiased and consistent and Least absolute deviation (LAD) estimator of $...
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Quantile regression estimator - conditions for consistency and efficiency

What are the conditions for consistency and efficiency of Quantile regression estimator (for example LAD) in a linear regression model?
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Why does quantile regression not work for the newsvendor model?

I want to use quantile regression to solve the newsvendor model for a critical fractile of 2/3. Surprisingly the quantile that minimizes the cost in my study is not the 2/3 quantile but the 80%. ...
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How do I select predictors for my quantile regression model?

I'm using a housing dataset that contains predictors such as # of bedrooms, bathrooms, car spots, distance from city center etc. to predict the price of sold houses. I'll be performing quantile ...
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38 views

Quantile regression does not give expected result regarding costs

I want to predict the length of an event. When I underestimate the event length it costs me 2€ (per minute) while an overestimation costs 1€ (per minute). To capture this price inbalance I tried using ...
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34 views

How to fill the bins?

Consider 1 million people earning money, sorted in increasing order. The kth decile, i.e. the kth 100,000 of them has an income share of $f(k)$ with $f(k)<f(k+1)$ and $\sum_{k=1}^{10} f(k)=1$. Let ...
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Quantile regression and mean log predictive score

During my research, I got stuck with an evaluation of my quantile regression models (qr). I have two QR models that model some economic variable in time. I would like to evaluate which model is better ...
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Assumptions of L1 Regression [duplicate]

I know that the L2 regression (regression-based L2 loss function/least square regression) assumptions are as follows. 1- Little or no Multicollinearity between the features. 2- Homoscedasticity ...
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How could one estimate $Y = X\beta \times \epsilon$ with $\epsilon \sim \text{Beta}(a,b)$?

Suppose the data generating process is $$Y_i=f(X_i)M_i.$$ where $M_i$~$Beta(a,b)$ and $f$ linear, for example,$f(X_i)=\alpha_0+\alpha_1X_i$. This is equivalent to $$M_i=Y_i/f(X_i).$$ I'm trying to ...
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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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71 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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202 views

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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169 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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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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210 views

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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38 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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166 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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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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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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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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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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62 views

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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134 views

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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191 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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239 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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72 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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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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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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105 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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176 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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117 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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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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900 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 \...