E. Mammen et S. Vandegeer, ESTIMATION OF FUNCTIONS WITH SPATIALLY INHOMOGENEOUS SMOOTHNESS - AN APPROACH BASED ON TOTAL VARIATION PENALTIES, Zeitschrift fur angewandte Mathematik und Mechanik, 76, 1996, pp. 139-142
Least squares penalized regression estimates with total variation pena
lties are considered. It a's shown that these estimators are least squ
ares splines with locally data adaptive placed knot points. Algorithms
and asymptotic statistical properties are discussed. The estimates ac
hieve optimal rates of convergence over bounded variation classes. Thi
s implies that the estimates adapt well to spatially inhomogeneous smo
othness.