Smooth tail index estimation

Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0]. Replacing the order statistics in tail index estimators by their corresponding quantiles from the distribution function that is based on the estimated log-concave density leads to novel smooth quantile and tail index estimators. These new estimators aim at estimating the tail index especially in small samples. Acting as a smoother of the empirical distribution function, the log-concave distribution function estimator reduces estimation variability to a much greater extent than it introduces bias. As a consequence, Monte Carlo simulations demonstrate that the smoothed version of the estimators are well superior to their non-smoothed counterparts, in terms of mean squared error.Comment: 17 pages, 5 figures. Slightly changed Pickand's estimator, added some more introduction and discussio

A second Marshall inequality in convex estimation

We prove a second Marshall inequality for adaptive convex density estimation via least squares. The result completes the first inequality proved recently by Du¨ mbgen et al. [2007. Marshall’s lemma for convex density estimation. IMS Lecture Notes—Monograph Series, submitted for publication. Preprint available at hhttp://arxiv.org/abs/math.ST/0609277i], and is very similar to the original Marshall inequality in monotone estimation

Modelling individual fertility levels in Malawian women: a spatial semiparametric regression model

Bayesian, Children ever born, Clustering, Fertility levels, Malawi, Poisson regression, Spatial modelling,

Exploratory Analysis of Spatial Patterns in Brazil’s Fertility Transition

Brazil, Development, Fertility change, Social diffusion, Spatial patterns,