Editing Median (section)

===Median–median line===

This is a method of robust regression. The idea dates back to [[Abraham Wald|Wald]] in 1940 who suggested dividing a set of bivariate data into two halves depending on the value of the independent parameter <math>x</math>: a left half with values less than the median and a right half with values greater than the median.<ref name=Wald1940>{{cite journal |last=Wald |first=A. |year=1940 |title=The Fitting of Straight Lines if Both Variables are Subject to Error |journal=[[Annals of Mathematical Statistics]] |volume=11 |issue=3 |pages=282–300 |jstor=2235677 |doi=10.1214/aoms/1177731868 |url=http://dml.cz/bitstream/handle/10338.dmlcz/103573/AplMat_20-1975-2_3.pdf |doi-access=free }}</ref> He suggested taking the means of the dependent <math>y</math> and independent <math>x</math> variables of the left and the right halves and estimating the slope of the line joining these two points. The line could then be adjusted to fit the majority of the points in the data set.

Nair and Shrivastava in 1942 suggested a similar idea but instead advocated dividing the sample into three equal parts before calculating the means of the subsamples.<ref name=Nair1942>{{cite journal |title=On a Simple Method of Curve Fitting |first1=K. R. |last1=Nair |first2=M. P. |last2=Shrivastava |journal=Sankhyā: The Indian Journal of Statistics |volume=6 |issue=2 |year=1942 |pages=121–132 |jstor=25047749 }}</ref> Brown and Mood in 1951 proposed the idea of using the medians of two subsamples rather the means.<ref name=Brown1951>{{cite book |last1=Brown |first1=G. W. |last2=Mood |first2=A. M. |year=1951 |chapter=On Median Tests for Linear Hypotheses |title=Proc Second Berkeley Symposium on Mathematical Statistics and Probability |location=Berkeley, CA |publisher=University of California Press |pages=159–166 |zbl=0045.08606 }}</ref> Tukey combined these ideas and recommended dividing the sample into three equal size subsamples and estimating the line based on the medians of the subsamples.<ref name=Tukey1971>{{cite book |last=Tukey |first=J. W. |year=1977 |title=Exploratory Data Analysis |location=Reading, MA |publisher=Addison-Wesley |isbn=0201076160 |url=https://archive.org/details/exploratorydataa00tuke_0 }}</ref>