The majority of empirical research in economics ignores the potential benefits of
nonparametric methods, while the majority of advances in nonparametric theory ignores the …

Summary Let X 1,…, X n be independent and identically distributed random vectors with a
(Lebesgue) density f. We first prove that, with probability 1, there is a unique log-concave …

Nonparametric smoothing under shape constraints has recently received much well-
deserved attention. Powerful methods have been proposed for imposing a single shape …

The estimation of probability density functions is one of the fundamental aspects of any
statistical inference. Many data analyses are based on an assumed family of parametric …

We study the smoothed log-concave maximum likelihood estimator of a probability
distribution on ℝd. This is a fully automatic nonparametric density estimator, obtained as a …

Economic conditions such as convexity, homogeneity, homotheticity, and monotonicity are
all important assumptions or consequences of assumptions of economic functionals to be …

Substantial structure and restrictions, such as monotonicity and curvature constraints,
necessary to give economic interpretation to empirical findings are often furnished by …

Research in the field of nonparametric shape constrained regression has been intensive.
However, only few publications explicitly deal with unimodality although there is need for …

Motivated by both the shortcomings of high order density estimators, and the increasingly
large data sets in many areas of modern science, we introduce new high order, non …

We discuss a robust data sharpening method for rendering a standard kernel estimator, with
a given bandwidth, unimodal. It has theoretical and numerical properties of the type that one …