ECE 901 Lecture 4: Estimation of Lipschitz smooth functions
نویسنده
چکیده
Consider the following setting. Let Y = f∗(X) +W, where X is a random variable (r.v.) on X = [0, 1], W is a r.v. on Y = R, independent of X and satisfying E[W ] = 0 and E[W ] = σ <∞. Finally let f∗ : [0, 1]→ R be a function satisfying |f∗(t)− f∗(s)| ≤ L|t− s|, ∀t, s ∈ [0, 1], (1) where L > 0 is a constant. A function satisfying condition (1) is said to be Lipschitz on [0, 1]. Notice that such a function must be continuous, but it is not necessarily differentiable. An example of such a function is depicted in Figure (a).
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