In this post I will provide R code that implement’s the combination of repeated running quantile with the LOESS smoother to create a type of “quantile LOESS” (e.g: “Local Quantile Regression”).

This method is useful when the need arise to fit robust and resistant ~~(Need to be verified)~~ a smoothed line for a quantile (an example for such a case is provided at the end of this post).

If you wish to use the function in your own code, simply run inside your R console the following line:

source("http://www.r-statistics.com/wp-content/uploads/2010/04/Quantile.loess_.r.txt") |

### Background

I came a cross this idea in an article titled “High throughput data analysis in behavioral genetics” by Anat Sakov, Ilan Golani, Dina Lipkind and my advisor Yoav Benjamini. From the abstract:

In recent years, a growing need has arisen in different fields, for the development of computational systems for automated analysis of large amounts of data (high-throughput). Dealing with non-standard noise structure and outliers, that could have been detected and corrected in manual analysis, must now be built into the system with the aid of robust methods. [...] we use a non-standard mix of robust and resistant methods: LOWESS and repeated running median.

The motivation for this technique came from “Path data” (of mice) which is

prone to suffer from noise and outliers. During progression a tracking system might lose track of the animal, inserting (occasionally very large) outliers into the data. During lingering, and even more so during arrests, outliers are rare, but the recording noise is large relative to the actual size of the movement. The statistical implications are that the two types of behavior require different degrees of smoothing and resistance. An additional complication is that the two interchange many times throughout a session. As a result, the statistical solution adopted needs not only to smooth the data, but also to recognize, adaptively, when there are arrests. To the best of our knowledge, no single existing smoothing technique has yet been able to fulfill this dual task. We elaborate on the sources of noise, and propose a mix of LOWESS (Cleveland, 1977) and the repeated running median (RRM; Tukey, 1977) to cope with these challenges

**If all we wanted to do was to perform moving average (running average) on the data, using R, we could simply use the rollmean function from the zoo package.**

But since we wanted also to allow quantile smoothing, we turned to use the rollapply function.

### R function for performing Quantile LOESS

Here is the R function that implements the LOESS smoothed repeated running quantile (with implementation for using this with a simple implementation for using average instead of quantile):