An Edgeworth expansion for finite population L-statistics

In this paper, we consider the one-term Edgeworth expansion for finite population L-statistics. We provide an explicit formula for the Edgeworth correction term and give sufficient conditions for the validity of the expansion which are expressed in terms of the weight function that defines the statistics and moment conditions.Comment: 14 pages. Minor revisions. Some explanatory comments and a numerical example were added. Lith. Math. J. (to appear

Design of a randomised controlled trial on immune effects of acidic and neutral oligosaccharides in the nutrition of preterm infants: carrot study

<p>Abstract</p> <p>Background</p> <p>Prevention of serious infections in preterm infants is a challenge, since prematurity and low birth weight often requires many interventions and high utility of devices. Furthermore, the possibility to administer enteral nutrition is limited due to immaturity of the gastrointestinal tract in the presence of a developing immune system. In combination with delayed intestinal bacterial colonisation compared with term infants, this may increase the risk for serious infections. Acidic and neutral oligosaccharides play an important role in the development of the immune system, intestinal bacterial colonisation and functional integrity of the gut. This trial aims to determine the effect of enteral supplementation of acidic and neutral oligosaccharides on infectious morbidity (primary outcome), immune response to immunizations, feeding tolerance and short-term and long-term outcome in preterm infants. In addition, an attempt is made to elucidate the role of acidic and neutral oligosaccharides in postnatal modulation of the immune response and postnatal adaptation of the gut.</p> <p>Methods/Design</p> <p>In a double-blind placebo controlled randomised trial, 120 preterm infants (gestational age <32 weeks and/or birth weight <1500 gram) are randomly allocated to receive enteral acidic and neutral oligosaccharides supplementation (20%/80%) or placebo supplementation (maltodextrin) between day 3 and 30 of life. Primary outcome is infectious morbidity (defined as the incidence of serious infections). The role of acidic and neutral oligosaccharides in modulation of the immune response is investigated by determining the immune response to DTaP-IPV-Hib(-HBV)+PCV7 immunizations, plasma cytokine concentrations, faecal Calprotectin and IL-8. The effect of enteral acidic and neutral oligosaccharides supplementation on postnatal adaptation of the gut is investigated by measuring feeding tolerance, intestinal permeability, intestinal viscosity, and determining intestinal microflora. Furthermore, short-term and long-term outcome are evaluated.</p> <p>Discussion</p> <p>Especially preterm infants, who are at increased risk for serious infections, may benefit from supplementation of prebiotics. Most studies with prebiotics only focus on the colonisation of the intestinal microflora. However, the pathways how prebiotics may influence the immune system are not yet fully understood. Studying the immune modulatory effects is complex because of the multicausal risk of infections in preterm infants. The combination of neutral oligosaccharides with acidic oligosaccharides may have an increased beneficial effect on the immune system. Increased insight in the effects of prebiotics on the developing immune system may help to decrease the (infectious) morbidity and mortality in preterm infants.</p> <p>Trial registration</p> <p>Current Controlled Trials ISRCTN16211826.</p

On conditional skewness with applications to environmental data

The statistical literature contains many univariate and multivariate skewness measures that allow two datasets to be compared, some of which are defined in terms of quantile values. In most situations, the comparison between two random vectors focuses on univariate comparisons of conditional random variables truncated in quantiles; this kind of comparison is of particular interest in the environmental sciences. In this work, we describe a new approach to comparing skewness in terms of the univariate convex transform ordering proposed by van Zwet (Convex transformations of random variables. Mathematical Centre Tracts, Amsterdam, 1964), associated with skewness as well as concentration. The key to these comparisons is the underlying dependence structure of the random vectors. Below we describe graphical tools and use several examples to illustrate these comparisons.The research of Félix Belzunce, Julio Mulero and José María Ruíz is partially funded by the Ministerio de Economía y Competitividad (Spain) under Grant MTM2012-34023-FEDER. Alfonso Suárez-Llorens acknowledges support received from the Ministerio de Economía y Competitividad (Spain) under Grant MTM2014-57559-P

On the minimal travel time needed to collect n items on a circle

Consider n items located randomly on a circle of length 1. The locations of the items are assumed to be independent and uniformly distributed on [0, 1). A picker starts at point 0, and he has to collect all n items by moving along the circle at unit speed in either direction. In this paper we study the minimal travel time of the picker. We obtain upper bounds and analyze the exact travel time distribution. Further, we derive closed-form limiting results when n tends to infinity. We determine the behavior of the limiting distribution in a positive neighbourhood of zero. The limiting distribution is closely related to exponential functionals associated with a Poisson process. These functionals occur in many areas and have been intensively studied in recent literature

An Edgeworth expansion for symmetric statistics

Bentkus V, Götze F, van Zwet WR. An Edgeworth expansion for symmetric statistics. ANNALS OF STATISTICS. 1997;25(2):851-896.We consider asymptotically normal statistics which are symmetric functions of N i.i.d. random variables. For these statistics we prove the validity of an Edgeworth expansion with remainder O(N-1) under Cramer's condition on the linear part of the statistic and moment assumptions for all parts of the statistic. By means of a counterexample we show that it is generally not possible to obtain an Edgeworth expansion with remainder o(N-1) without imposing additional assumptions on the structure of the nonlinear part of the statistic

An Edgeworth expansion for symmetric statistics

Bentkus V, Götze F, van Zwet WR. An Edgeworth expansion for symmetric statistics. ANNALS OF STATISTICS. 1997;25(2):851-896.We consider asymptotically normal statistics which are symmetric functions of N i.i.d. random variables. For these statistics we prove the validity of an Edgeworth expansion with remainder O(N-1) under Cramer's condition on the linear part of the statistic and moment assumptions for all parts of the statistic. By means of a counterexample we show that it is generally not possible to obtain an Edgeworth expansion with remainder o(N-1) without imposing additional assumptions on the structure of the nonlinear part of the statistic