  Statistical modeling of experimental physical laws is based on the
probability density function of measured variables. It is expressed by
experimental data via a kernel estimator. The kernel is determined objectively
by the scattering of data during calibration of experimental setup. A physical
law, which relates measured variables, is optimally extracted from experimental
data by the conditional average estimator. It is derived directly from the
kernel estimator and corresponds to a general nonparametric regression. The
proposed method is demonstrated by the modeling of a return map of noisy
chaotic data. In this example, the nonparametric regression is used to predict
a future value of chaotic time series from the present one. The mean predictor
error is used in the definition of predictor quality, while the redundancy is
expressed by the mean square distance between data points. Both statistics are
used in a new definition of predictor cost function. From the minimum of the
predictor cost function, a proper number of data in the model is estimated.
