Let X = (X1, X2, ...) be a non-deterministic infinite exchangeable sequence with values in {0, 1}. We show that X is Hoeffding-decomposable if, and only if, X is either an i.i.d. sequence or a Pólya sequence. This completes the results established in Peccati [2004]. The proof uses several combinatorial implications of the correspondence between Hoeffding decomposability and weak independence. Our results must be compared with previous characterizations of i.i.d. and Pólya sequences given by Hill et al. [1987] and Diaconis and Yilvisaker [1979] .

We study Hoeffding decomposable exchangeable sequences with values in a finite setWe provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, for every K ≥ 3, there exists a class of neither Pólya nor i.i.d. D-valued exchangeable sequences that are Hoeffding decomposable.

Accurate estimation of wind speed probability density at a given site is crucial in maximising the yield of a wind farm. This goal calls for devising probabilistic models with adaptive algorithms that accurately fit wind speed distributions. In this study, a non-parametric combinatorial method is implemented for obtaining an accurate non-parametric kernel density estimation (KDE)-based statistical model of wind speed, in which the selection of the bandwidth parameter is optimised concerning mean integrated absolute error (L 1 error) between the true and hypothesised densities. The proposed model is compared with three popular parametric models and Rule of Thumb-based KDE model using standard goodness-of-fit and statistical tests. Results confirm the suitability of KDE methods for wind speed modelling and the accuracy of the proposed implemented combinatorial method. It is worthwhile mentioning that the implemented procedure is adaptive (i.e. data driven) and robust. Nomenclature Symbols X random variable f X probability density function of X

In this article, we obtain some uniform laws of large numbers and functional central limit theorems for sequential empirical measure processes indexed by classes of product functions satisfying appropriate Vapnik-Červonenkis properties.