Advanced Methods of Physiological System Modeling pp 229-242 | Cite as

# On Kernel Estimation Using Non-Gaussian and/or Non-White Input Data

## Abstract

In many actual applications of the Volterra-Wiener approach, the prevailing conditions are less than ideal ie., the input-output data are contaminated by noise and/or the available input data deviate from the Gaussian white noise archetype required by Wiener’s theory. Deviations from whiteness and/orGaussianness may be ca used by experimental necessity or inadvertent stimulus distortion. At the same time, experimen tal and/or computational expediencies have led to the introduction of non-Gaussian multi-level (e.g., binary, ternary, etc.) or multi-frequency quasi-white (i.e., approximately white) input signals. Since the original (and most widely used to date) kernel estimation technique is based on input-output crosscorrelations and requires input whiteness (or, at least, quasi-whiteness), extensive efforts have been made to adapt this crosscorrelation technique to non-Gaussian (but quasi-white) inputs. These efforts have led to successful adaptations of the cross-correlation technique to several classes of non-Gaussian quasi-white inputs, although certain restrictions apply in some cases (e.g., binary white inputs cannot estimate diagonal kernel values). More recent techniques are based on least-squares estimation methods and obviate the need for input whiteness or Gaussianness, although they may still impose certain restrictions (e.g., sufficiently broadband inputs are required and the estima ted models must be complete). The Laguerre expansion technique (Marmarelis, 1993) belongs to this latter category and overcomes the limitations imposed by the crosscorrelation technique in the case of non-Gaussian or non-white inputs, allowing accurate kernel estimation under previously prohibitive conditions (e.g., diagonal kernel values can now be estimated with binary inputs). This paper demonstrates the expanded capabilities of kernel estimation using Laguerre expansions when the input is non-Gaussian and/or non-white, enlarging the scope of Volterra-Wiener analysis in actual applications.

## Keywords

Kernel Estimate Volterra Kernel Cross Correlation Technique Binary Input Wiener Kernel## Preview

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