Quantile regression for trend analysis

Quantile regression extends ordinary least-squares regression to quantiles of the response variable. Ordinary regression is a model for the conditional mean, where the mean is conditional on the value of the explanatory variable. Likewise, quantile regression is a model for the conditional quantiles. For trend analysis the explanatory variable is time. Quantiles are points taken at regular intervals from the cumulative distribution function of a random variable. The quantiles mark a set of ordered data into equal-sized data subsets.