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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regression quntile [duplicate]

How can we tell which of the two equations in quantile of 0.05 and 0.95 with the same variables as the original equation for analysis should be chosen? r1=-2.8037+0.2433r2+0.4387r3+0.2011r4+1.1313r5 ...
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quantile regression question [closed]

How can we guess which one of a quantile regression equation between several quantile is better and we can choose that.for example if we have 2 equation : ...
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18 views

Using quantile regression with a linear equation bounded by 1

I am trying to replicate the research of Ducey and Knapp (2010)* with my own data using the quantreg package in R. My question/problem might be algebraic rather than statistical, but I thought I would ...
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31 views

Are there multiple ways to interpret the slope parameters in linear regression?

I am struggling to understand an interpretation of regression parameters presented in a paper comparing and contrasting OLS regression to quantile regression. The authors present an example linear ...
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A question in proof from “Regression Quantiles” by Roger Koenker and Gilbert Bassett(Econometrica, 1978)

I have a problem in verifying the conclusion (3.5) in proving Theorem 3.3 as attached here. Particularly, from (3.4) \begin{align} 0&<\sum_{k=1}^{K}[(1/2-\theta)v_{k}+|v_{k}|]\\ ...
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A question in directional derivatives of a quantile regression object function

The question comes from the paper ``Regression Quantiles'' by Roger Koenker and Gilbert Bassett(Econometrica, 1978). $0< \theta <1$. Define $\psi(b;\theta,y,X)=\sum^{T}_{t=1}[\theta-1/2+1/2 \; ...
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273 views

r-squared in quantile regression

I am using quantile regression to find predictors of 90th percentile of my data. I am doing this in R using the quantreg package. How can I determine $r^2$ for ...
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70 views

Testing for statistical differences of quantile regression line slopes

If I were to compare the statistical similarity between the slopes of OLS regression lines from two independent samples, I would use a t-test to test if the slopes are equal or not. I'd like to ...
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125 views

Is it valid to use quantile regression with only categorical predictors?

I am new to quantile regression and most of the examples I see are in a multiple regression context with continuous predictors. I am analyzing a designed experiment and was wondering if quantile ...
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38 views

Posterior simulations in quantile regression

I'm fitting quantile regression models and would like to do posterior simulations from the fitted models, i.e. generating new random data which could arise from the model. I would know how to do this ...
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1answer
64 views

Marginal Effects of Discrete Variables in Quantile Regression

I find myself puzzled by a passage about marginal effects of discrete variables in quantile regression. On p. 217 of Cameron and Trivedi's MUS book, the authors write: For the $j$th (continuous) ...
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GAM-style effects plots for interpreting qrnn model

how to analyse GAM-style effects plots for interpreting qrnn models. I couldn't quite understand it from R documentation.
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Hausman test for quantile regressions

I would like to know whether I can compare instrumental variables quantile estimates, for instance using the the Chernozhukov and Hansen (2006) IVQR estimator (or quantile regression with fixed ...
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46 views

Comparing medians

I am interested in comparing the medians of a continuous random variable across two groups. One option is to do a chi-square-based median test - in stata run median var, by(group). The other option is ...
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21 views

How to Predict using Quantile Regression [duplicate]

Were you able to figure out your question about what quantile prediction to use for the forecasting purposes? Different quantile regressions produce different estimates.
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64 views

Quantile regression with censored data. Quantiles not fitted

I'm trying to fit a quantile regression model for rigth censoring data and I'm using R with the package quantreg and its function crq. I'm trying the Portnoy method that it's suposed to estimate the ...
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31 views

Interpretation of quantile regression with discrete variables, whole sample vs subsample

I am trying to run a (conditional) quantile regression, my outcome $(Y)$ is income, and my regressors $(X)$ are all discrete. My question is what are the differences if, when I focus on one particual ...
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89 views

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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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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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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142 views

Errors in fitting a censored quantile regression model

I have an outcome with right censoring like this: ...
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86 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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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 ...
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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 ...
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70 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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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 ...
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132 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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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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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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38 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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256 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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24 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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145 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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55 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 ...
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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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37 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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143 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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502 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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129 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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47 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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282 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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473 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
168 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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186 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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149 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
354 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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245 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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Simulation about quantile regression

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