function result=hl(x)
%HL computes the Hodges-Lehmann location estimate on the columns of x.
% The Hodges-Lehmann estimator is defined as
% hl(x)=med {(x_i + x_j)/2} with 1<=i<j<=n
% It can resist about 29% outliers.
% If x is a matrix, the location estimate is computed on the columns of x. The
% result is then a row vector. If x is a row or a column vector,
% the output is a scalar.
%
% The behavior of the HL estimator in small samples is discussed in:
% Rousseeuw, P.J. and Verboven, S. (2002),
% "Robust estimation in very small samples",
% Computational Statistics and Data Analysis, 40, 741-758.
%
% Required input argument:
% x: either a data matrix with n observations in rows, p variables in columns
% or a vector of length n.
%
% I/O: result=hl(x);
%
% This function is part of LIBRA: the Matlab Library for Robust Analysis,
% available at:
% http://wis.kuleuven.be/stat/robust.html
%
% Written by S. Verboven
% Last revision: 28/08/03 by N. Smets
[n,p]=size(x);
if n==1 & p==1
result=x; %when X is a one by one matrix, all location estimators must be equal to that matrix
return
elseif n==1
x=x'; %we only want to work with column vectors
n=p;
p=1;
end
if n==2
result=mean(x,1); % all location estimators must equal to the average for n=2
return
end
for k=1:p
m=0;
y=zeros(1,n*(n-1)/2); %initializing help vector
X=x(:,k);
for i=1:n %calculating all possible pairwise means
for j=(i+1):n
m=m+1;
y(m)=(X(i)+X(j))/2;
end
end
result(k)=median(y);
y=[]; %clear help vector
end