Kernel regression estimators for signal recovery

M. Pawlak and U. Stadtmüller

Statistics & Probability Letters, 1997, vol. 31, issue 3, 185-198

Abstract: We consider the problem of estimating a class of smooth functions defined everywhere on a real line utilizing nonparametric kernel regression estimators. Such functions have an interpretation as signals and are common in communication theory. Furthermore, they have finite energy, bounded frequency content and often are jammed by noise. We examine the expected L2-error of two types of estimators, one is a classical kernel regression estimator utilizing kernel functions of order p, p [greater-or-equal, slanted] 2 and the other one is motivated by the Whittaker-Shannon sampling expansion. The latter estimator employs a non-integrable kernel function sin(t)/nt, t [epsilon] . The comparison shows that the second technique outperforms the first one as long as the frequency band is finite.

Keywords: Signal; theory; Nonparametric; regression; Band-limited; signals; Kernel; estimators; Cardinal; expansions; Rate; of; convergence (search for similar items in EconPapers)
Date: 1997
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