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Asymptotic Minimax Risk for the White Noise Model on the Sphere
Author(s) -
Klemela Jussi
Publication year - 1999
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00160
Subject(s) - mathematics , minimax , white noise , additive white gaussian noise , unit sphere , norm (philosophy) , euclidean space , gaussian noise , asymptotic formula , function (biology) , mathematical analysis , mathematical optimization , statistics , algorithm , law , evolutionary biology , biology , political science
Estimation of an unknown function on the unit sphere of the Euclidean space is considered. The function is observed in Gaussian continuous time white noise. Uniform norm is chosen as a loss function and exact asymptotic minimax risk is derived extending the result of Korostelev (1993). The exact asymptotic minimax risk is also given for the L 2 ‐loss, applying the result of Pinsker (1980).