Cross validation, spline

The desirable number of knots and degrees of polynomial pieces can be estimated using cross-validation. An initial value for s can be n/7 or / n) for n > 100 where n is the number of data points. Quadratic splines can be used for data without inflection points, while cubic splines provide a general approximation for most continuous data. To prevent over-fitting data with... 

The crossover modulus is the value of G (and G") at the frequency where the two moduli are equal, i.e, where the curves of G co) and G (o) cross (see Fig. 5.5). An objective identification of the crossover point can be made by fitting the points on both curves in the vicinity of this point with cubic splines. Bafna [35] has pointed out that this empirical correlation is based on data for a single family of polypropylenes, i.e. a group of polymers having similar molecular weight distributions, and that it cannot be expected to be valid for other groups of polymers. 

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