ESTIMATION OF FUNCTIONS WITH SPATIALLY INHOMOGENEOUS SMOOTHNESS - AN APPROACH BASED ON TOTAL VARIATION PENALTIES

Authors
MAMMEN E VANDEGEER S
Citation
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
Citations number
10
Categorie Soggetti
Mathematics,"Mathematical Method, Physical Science",Mechanics,Mathematics
Journal title
Zeitschrift fur angewandte Mathematik und Mechanik → ACNP
ISSN journal
00442267
Volume
76
Year of publication
1996
Supplement
3
Pages
139 - 142
Database
ISI
SICI code
0044-2267(1996)76:<139:EOFWSI>2.0.ZU;2-G
Abstract
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.