Figure 1.

Visualization of the RR-BLUP estimator (<a onClick="popup('http://www.biomedcentral.com/1471-2164/13/452/mathml/M12','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2164/13/452/mathml/M12">View MathML</a>) and the LASSO estimator (<a onClick="popup('http://www.biomedcentral.com/1471-2164/13/452/mathml/M13','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2164/13/452/mathml/M13">View MathML</a>) as solutions to a least-squares problem with different penalization [[38],[39]]. We illustrate a two-dimensional case. The blue ellipses show the contours of the RSS function around the ordinary least-square solution (<a onClick="popup('http://www.biomedcentral.com/1471-2164/13/452/mathml/M14','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2164/13/452/mathml/M14">View MathML</a>). The ridge estimator is the point at which the innermost elliptical contour touches the circular ridge penalty <a onClick="popup('http://www.biomedcentral.com/1471-2164/13/452/mathml/M15','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2164/13/452/mathml/M15">View MathML</a>. The LASSO estimator is the point at which the innermost elliptical contour touches the diamond shaped LASSO penalty |u1| + |u2|<cL. Contrary to the ridge penalty, the LASSO penalty allows estimations to be exactly zero.

Riedelsheimer et al. BMC Genomics 2012 13:452   doi:10.1186/1471-2164-13-452
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