کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5129331 1489640 2017 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Nonparametric estimation of a function from noiseless observations at random points
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز عددی
پیش نمایش صفحه اول مقاله
Nonparametric estimation of a function from noiseless observations at random points
چکیده انگلیسی

In this paper we study the problem of estimating a function from n noiseless observations of function values at randomly chosen points. These points are independent copies of a random variable whose density is bounded away from zero on the unit cube and vanishes outside. The function to be estimated is assumed to be (p,C)-smooth, i.e., (roughly speaking) it is p times continuously differentiable. Our main results are that the supremum norm error of a suitably defined spline estimate is bounded in probability by {ln(n)∕n}p∕d for arbitrary p and d and that this rate of convergence is optimal in minimax sense.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 160, August 2017, Pages 93-104
نویسندگان
, , , , ,