Nonparametric Estimates of the Asymptotic Covariance Matrix Associated with BICKEL's Estimate for Multivariate Shift Parameters

Nonparametric estimates are proposed for the asymptotic covariance matrix associated with the vector of medians of averages of pairs when estimating the shift parameter in the multivariate one sample problem. These estimates are based on density estimation and are competitors to the “natural” estimate proposed by BICKEL (1965). Weak and strong consistency of the estimates as well as asymptotic normality are presented.     

On the Theory for RYANS Universal Multiple Comparison Procedure with Treatment of Ties in the Ranks of Samples

The proposal of RYAN (1960) for multiple comparison procedures has not become well known despite of its universal applicability. Only his idea of adjusted levels has been used in a modified manner, cf. EINOT and GABRIEL (1975), WELSCH (1977), RAMSEY (1978). This article re-introduces the procedure and demonstrates its broad applicability also as a nonparametric method. Above all an exact mathematical foundation is aspired. The case of ties in the ranks of samples has been taken into consideration.     

Age-related change in breeding performance in early life is associated with an increase in competence in the migratory barn swallow Hirundo rustica

1. We investigated age-related changes in two reproductive traits (laying date and annual fecundity) in barn swallows Hirundo rustica L. using a mixed model approach to di-stinguish among between- and within-individual changes in breeding performance with age. 2. We tested predictions of age-related improvements of competence (i.e. constraint hypothesis) and age-related progressive disappearance of poor-quality breeders (i.e. selection hypothesis) to explain age-related increase in breeding performance in early life. 3. Reproductive success increased in early life, reaching a plateau at middle age (e.g. at 3 years of age) and decreasing at older age (> 4 years). Age-related changes in breeding success were due mainly to an effect of female age. 4. Age of both female and male affected timing of reproduction. Final linear mixed effect models (LME) for laying date included main and quadratic terms for female and male age, suggesting a deterioration in reproductive performance at older age for both males and females. 5. We found evidence supporting the constraints hypothesis that increases in competence within individuals, with ageing being the most probable cause of the observed increase in breeding performance with age in early life. Two mechanisms were implicated: (1) advance in male arrival date with age provided middle-aged males with better access to mates. Yearling males arrived later to the breeding grounds and therefore had limited access to high-quality mates. (2) Breeding pairs maintaining bonds for 2 consecutive years (experienced pairs) had higher fecundity than newly formed inexperienced breeding pairs. 6. There was no support for the selection hypothesis because breeding performance was not correlated with life span. 7. We found a within-individual deterioration in breeding and migratory performance (arrival date) in the oldest age-classes consistent with senescence in these reproductive and migratory traits.