Abstract: We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in R. Our study covers both the case where the true underlying density is log-concave, and where this model is misspecified. We begin by showing that for a sequence of log-concave densities, convergence in distribution implies much s...

We prove a version of Hrushovski's 1989 results on almost orthogonal regular types in the context of simple and superstable nitary abstract elementary classes: from a certain expression of `non-orthogonality' we can conclude the existence of a group acting on the geometry obtained on the set of realizations of a regular Lascar strong type, and if we rule out the presence of a non-classical grou...

In this paper, we introduce and study a new iterative scheme toapproximate a common xed point for a nite family of generalized asymptoticallyquasi-nonexpansive nonself-mappings in Banach spaces. Several strong and weakconvergence theorems of the proposed iteration are established. The main resultsobtained in this paper generalize and rene some known results in the currentliterature.