Bashar Almansour
Quantile Regression:Purpose: Quantile regression is a statistical method used to estimate the conditional quantiles of a response variable given certain values of predictor variables. In other words, it allows you to model different quantiles of the response distribution, providing a more comprehensive view of the relationship between variables compared to traditional mean regression. Methodology: Instead of modelling the conditional mean of the response variable (as in ordinary least squares regression), quantile regression models various quantiles (e.g., median, 25th percentile, 75th percentile) of the response variable. This is particularly useful when the distribution of the response variable is not symmetric or when you want to capture different parts of the distribution. Quantile-on-Quantile Regression:Purpose: Quantile-on-quantile regression is a more advanced technique that involves estimating the conditional quantiles of one response variable based on the conditional quantiles of another response variable. It allows you to investigate the relationship between two variables across different quantiles of their respective distributions. Methodology: Instead of modelling a single conditional quantile, quantile-on-quantile regression estimates the conditional quantiles of one variable as a function of the conditional quantiles of another variable. This can provide insights into how the relationship between the two variables varies across different parts of their distributions.
Quantile regression and quantile-on-quantile regression are related statistical techniques, but they have distinct purposes and methodologies.
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