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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 134727, 8 pages
http://dx.doi.org/10.1155/2013/134727
Research Article

Coefficient-Based Regression with Non-Identical Unbounded Sampling

School of Mathematics and Computational Science, Guangdong University of Business Studies, Guangzhou, Guangdong 510320, China

Received 18 January 2013; Accepted 15 April 2013

Academic Editor: Qiang Wu

Copyright © 2013 Jia Cai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate a coefficient-based least squares regression problem with indefinite kernels from non-identical unbounded sampling processes. Here non-identical unbounded sampling means the samples are drawn independently but not identically from unbounded sampling processes. The kernel is not necessarily symmetric or positive semi-definite. This leads to additional difficulty in the error analysis. By introducing a suitable reproducing kernel Hilbert space (RKHS) and a suitable intermediate integral operator, elaborate analysis is presented by means of a novel technique for the sample error. This leads to satisfactory results.