A sharp adaptive confidence ball for self-similar functions
نویسندگان
چکیده
منابع مشابه
Adaptive Confidence Bands for Nonparametric Regression Functions.
A new formulation for the construction of adaptive confidence bands in non-parametric function estimation problems is proposed. Confidence bands are constructed which have size that adapts to the smoothness of the function while guaranteeing that both the relative excess mass of the function lying outside the band and the measure of the set of points where the function lies outside the band are...
متن کاملReconstruction of self - similar functions
We provide a solution to the problem of reconstructing a fractal interpolation function from its scale-space zeros. Every fractal interpolation function f has a graph that is the attractor of an iterated functions system deened by contractive maps w1; : : : ; wN. We construct approximations of these maps from ngerprints in scale-space.
متن کاملSupplement to “Adaptive Confidence Bands for Nonparametric Regression Functions”
This supplement contains the proofs of Theorem 2, Propositions 2 and 3, Lemma 1 and Eq.(14). 7 Proof of Theorem 2 Rather than prove Theorem 2 directly it is convenient to first prove an analogue of the Theorem in the context of multivariate Normal random vectors. This is done in section 7.1. The proof of Theorem 2 is then given in section 7.2 7.1 Confidence Bound For Multivariate Normal Vectors...
متن کاملAdaptive Confidence Intervals for Regression Functions Under Shape Constraints
Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in terms of an analytic quantity, the local modulus of continuity. This bound depends not only on the function but also the assumed function class. These benchm...
متن کاملSharp Inequalities for Polygamma Functions
where μ is a nonnegative measure on [0,∞) such that the integral (2) converges for all x > 0. This means that a function f(x) is completely monotonic on (0,∞) if and only if it is a Laplace transform of the measure μ. The completely monotonic functions have applications in different branches of mathematical sciences. For example, they play some role in combinatorics, numerical and asymptotic an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2016
ISSN: 0304-4149
DOI: 10.1016/j.spa.2016.04.017