ε-Entropy and moduli of smoothness in $L^{p}$-spaces

• Autorzy: A. Kamont
• Języki publikacji: EN

Abstrakty

EN

The asymptotic behaviour of ε-entropy of classes of Lipschitz functions in $L^p(𝕀^d)$ is obtained. Moreover, the asymptotics of ε-entropy of classes of Lipschitz functions in $L^p(ℝ^d)$ whose tail function decreases as $O(λ^{-γ})$ is obtained. In case p = 1 the relation between the ε-entropy of a given class of probability densities on $ℝ^d$ and the minimax risk for that class is discussed.

Kategorie tematyczne

• 41A29: Approximation with constraints
• 62G05: Estimation
• 41A63: Multidimensional problems (should also be assigned at least one other classification number in this section)
• 41A46: Approximation by arbitrary nonlinear expressions; widths and entropy
• 41A25: Rate of convergence, degree of approximation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 102
• Numer: 3
• Strony: 277-302

Daty

wydano

1992

otrzymano

1992-02-26

Twórcy

autor

A. Kamont

• Institute of Mathematics, Polish Academy of Sciences, Abrahama 18, 81-825 Sopot, Poland

Bibliografia

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