arXiv subjects

Omar El-Dakkak

Publications and source records attributed to Omar El-Dakkak.

4 recordsLinked to original sources

arXiv2012

Exchangeable Hoeffding decompositions over finite sets: a characterization and counterexamples

We study Hoeffding decomposable exchangeable sequences with values in a finite set D. We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, if the cardinality of D is strictly greater than 2, then there exists a class of neither Pólya nor i.i.d. D-valued exchangeable sequences that are Hoeffding decomposable. The construction of such sequences is based on some ideas appearing in Hill, Lane and Sudderth [1987] and answers a question left open in El-Dakkak and Peccati [2008].

math.PR↗

arXiv2009

Approximation for general bootstrap of empirical processes with an application to kernel-type density estimation

The purpose of this note is to provide an approximation for the generalized bootstrapped empirical process achieving the rate in Kolmos et al. (1975). The proof is based on much the same arguments as in Horvath et al. (2000). As a consequence, we establish an approximation of the bootstrapped kernel-type density estimator

math.ST↗

arXiv2008

Limit Behaviour of Sequential Empirical Measure Processes

In this paper, 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-Chervonenkis properties.

math.PR↗

arXiv2006

Hoeffding decompositions and two-colour urn sequences

Let X 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 Polya 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 Polya sequences given by Hill et al. [1987] and Diaconis and Yilvisaker [1979].

math.PR↗