Coefficient-Based Regression with Non-Identical Unbounded Sampling

Abstract EN

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.