کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1145650 1489677 2014 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Nonparametric estimation of multivariate elliptic densities via finite mixture sieves
ترجمه فارسی عنوان
برآورد غیر پارامتری تراکم بیضوی چند متغیره با استفاده از غربالگری مجدد
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز عددی
چکیده انگلیسی

This paper considers the class of pp-dimensional elliptic distributions (p≥1p≥1) satisfying the consistency property (Kano, 1994)  [23] and within this general framework presents a two-stage nonparametric estimator for the Lebesgue density based on Gaussian mixture sieves. Under the on-line Exponentiated Gradient (EG) algorithm of Helmbold et al. (1997)  [20] and without restricting the mixing measure to have compact support, the estimator produces estimates converging uniformly in probability to the true elliptic density at a rate that is independent of the dimension of the problem, hence circumventing the familiar curse of dimensionality inherent to many semiparametric estimators. The rate performance of our estimator depends on the tail behaviour of the underlying mixing density (and hence that of the data) rather than smoothness properties. In fact, our method achieves a rate of at least Op(n−1/4)Op(n−1/4), provided only some positive moment exists. When further moments exists, the rate improves reaching Op(n−3/8)Op(n−3/8) as the tails of the true density converge to those of a normal. Unlike the elliptic density estimator of Liebscher (2005)  [25], our sieve estimator always yields an estimate that is a valid density, and is also attractive from a practical perspective as it accepts data as a stream, thus significantly reducing computational and storage requirements. Monte Carlo experimentation indicates encouraging finite sample performance over a range of elliptic densities. The estimator is also implemented in a binary classification task using the well-known Wisconsin breast cancer dataset.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 123, January 2014, Pages 43–67
نویسندگان
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