How is quantile regression used in econometrics and statistics?

How is quantile regression used in econometrics and statistics?

Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares results in estimates of the conditional mean of the response variable given certain values of the predictor variables, quantile regression aims at estimating either the conditional median…

Do you have to estimate the conditional mean in Quantile Regression?

But we don’t have to always estimate the conditional mean. We could estimate the median, or the 0.25 quantile, or the 0.90 quantile. That’s where quantile regression comes in. The math under the hood is a little different, but the interpretation is basically the same.

How to use summary function in Quantile Regression?

We can use the summary function to extract details about the model. summary (qr1) Call: rq (formula = y ~ x, tau = 0.9, data = dat) tau: [1] 0.9 Coefficients: coefficients lower bd upper bd (Intercept) 6.04168 5.93265 6.39328 x 0.16125 0.15591 0.17826

Are there machine learning methods for quantile regression?

Beyond simple linear regression, there are several machine learning methods that can be extended to quantile regression. A switch from the squared error to the tilted absolute value loss function allows gradient descent based learning algorithms to learn a specified quantile instead of the mean.

Why do we use Laplacian likelihood in Quantile Regression?

Because quantile regression does not normally assume a parametric likelihood for the conditional distributions of Y|X, the Bayesian methods work with a working likelihood. A convenient choice is the asymmetric Laplacian likelihood, because the mode of the resulting posterior under a flat prior is the usual quantile regression estimates.

What is the conditional median of a LAD regression?

LAD regression estimates the conditional median (a conditional 0.50 quantile) of a dependent variable given the independent variable (s) by minimizing sums of absolute deviations between observed and predicted values.

Which is the censored version of quantile regression?

Censored Quantile Regression. This is the censored quantile regression model: estimated values can be obtained without making any distributional assumptions, but at the cost of computational difficulty, some of which can be avoided by using a simple three step censored quantile regression procedure as an approximation.

Is the conditional mean of quantile regression identifiable?

If the response variable is subject to censoring, the conditional mean is not identifiable without additional distributional assumptions, but the conditional quantile is often identifiable. For recent work on censored quantile regression, see: Portnoy and Wang and Wang

When does a quantile regression cross a line?

quantile regressions will cross as non-parallel lines are assured to do (in Euclidean geometry). Empirically and not surprisingly, these crossings are more likely at the edge of the data range or outside of it. They do however pose a challenge for interpretable predictions.

How do I interpret quantile regression coefficients for males?

With the binary predictor, the constant is median for group coded zero (males) and the coefficient is the difference in medians between males and female (see the tabstat above). Looking at the tabulated predicted scores we see that we get two values, the conditional median for males (52) and the conditional median for female (57).