Entropy estimate for high-dimensional monotonic functions
نویسندگان
چکیده
منابع مشابه
Entropy Estimate For High Dimensional Monotonic Functions
We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of d-dimensional bounded monotonic functions under L norms. It is interesting to see that both the metric entropy and bracketing entropy have different behaviors for p < d/(d − 1) and p > d/(d − 1). We apply the new bounds for bracketing entropy to establish a global rate of convergence of the MLE of ...
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This means that every F ∈ Fd satisfies: (i) (non-negativity). For finite intervals I = (a1, b1] × · · · × (ad, bd] ≡ (a, b], with a, b ∈ Rd, F (I) = ∆dF (a, b] ≥ 0 where ∆d denotes the d−dimensional difference operator. (ii) (continuity from above). If y ↓ x, then F (y) ↓ F (x). (iii) (normalization). If x1∧. . .∧xd → −∞, then F (x) → 0; if x1∧. . .∧xd → +∞, then F (x) → 1. (See Billingsley [4]...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 2007
ISSN: 0047-259X
DOI: 10.1016/j.jmva.2006.09.003