2010, Vol.13, No.1, pp.45-52

Statistical modeling of physical laws connects experiments with mathematical descriptions of natural phenomena. Most general modeling is based on nonparametric estimation of the probability density from statistical samples of measured variables. For this purpose a kernel estimator is utilized in the article. As an objective kernel the scattering function determined by calibration of the instrument is introduced. This function provides for a definition of experimental information and redundancy of experimentation in terms of information entropy. The redundancy increases with the number of experiments, while the experimental information converges to a value that describes the complexity of the data. The difference between the redundancy and the experimental information is proposed as the model cost function. From its minimum, a proper number of data needed for modeling is estimated. As an optimal, nonparametric estimator of the relation between measured variables the conditional average extracted from the kernel estimator is proposed. The modeling is demonstrated on noisy chaotic data.
Key words: kernel estimator, complexity, redundancy, model cost function, conditional average predictor, nonparemetric regression, predictor quality, noisy chaotic generator

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