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function [Xrls,yrls]=RLSregor(y,X) %Syntax: [xrls,yrls]=RLSregor(y,X) %_________________________________ % % Calculates the Reweighted Least Squares (RLS) regression data points % from the LMS regression (through the origin). % % Xrls is the X values matrix to be taken into account for RLS. % yrls is the y values vector to be taken into account for RLS. % y is the vector of the dependent variable. % X is the data matrix of the independent variable. % % Reference: % Rousseeuw PJ, Leroy AM (1987): Robust regression and outlier detection. Wiley. % % % Alexandros Leontitsis % Institute of Mathematics and Statistics % University of Kent at Canterbury % Canterbury % Kent, CT2 7NF % U.K. % % University e-mail: al10@ukc.ac.uk (until December 2002) % Lifetime e-mail: leoaleq@yahoo.com % Homepage: http://www.geocities.com/CapeCanaveral/Lab/1421 % % Sep 3, 2001. if nargin<1 | isempty(y)==1 error('Not enough input arguments.'); end % Estimate the LMS values if nargin<2 | isempty(X)==1 LMSout=LMSregor(y); X=(1:length(y))'; else LMSout=LMSregor(y,X); end % p is the number of parameters to be estimated p=size(X,2); % Calculate the residuals r=y-LMSout; % Estimate the preliminary scale parameter s=LMSsca(r,0,p); % Take into account a data point, if its residual is relatively small w=find(abs(r/s)<=2.5); Xrls=X(w,:); yrls=y(w);