Limit theorems for nondegenerate U-statistics of continuous semimartingales

This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

Tools & Techniques - Statistics: Propensity score techniques.

Propensity score (PS) techniques are useful if the number of potential confounding pretreatment variables is large and the number of analysed outcome events is rather small so that conventional multivariable adjustment is hardly feasible. Only pretreatment characteristics should be chosen to derive PS, and only when they are probably associated with outcome. A careful visual inspection of PS will help to identify areas of no or minimal overlap, which suggests residual confounding, and trimming of the data according to the distribution of PS will help to minimise residual confounding. Standardised differences in pretreatment characteristics provide a useful check of the success of the PS technique employed. As with conventional multivariable adjustment, PS techniques cannot account for confounding variables that are not or are only imperfectly measured, and no PS technique is a substitute for an adequately designed randomised trial.

Ethnic Diversity, Social Trust and the Moderating Role of Integration Policy

Increasing ethnic diversity and whether or not it impacts on trust are highly debated topics. Numerous studies report a negative relationship between diversity and trust, particularly in the US. A growing body of follow-up studies examined the extent to which these findings can be transferred to Europe, but the results remain inconclusive. Moving beyond the discussion of the mere existence or absence of diversity effects on trust, this study is concerned with the moderation of this relationship: It addresses the neglected role of subnational integration policies influencing diversity’s impact on trust. Empirical tests not only indicate that integration policies moderate the relationship, but also suggest that the influence of policies varies substantively according to the specific policy aspect under consideration.

Ethnic disparity in defensive coping endothelial responses: The SABPA study

OBJECTIVES Defensive coping (DefS) in Blacks has been associated with greater cardiovascular risk than in their White counterparts. We examined associations between endothelial function mental stress responses and markers of vascular structure in a bi-ethnic cohort. METHODS We examined vascular function and structure in 368 Black (43.84±8.31years) and White Africans (44.78±10.90years). Fasting blood samples, 24h blood pressure, left carotid intima-media thickness of the far wall (L-CIMTf), and left carotid cross-sectional wall area (L-CSWA) values were obtained. von Willebrand factor (VWF), endothelin-1 (ET-1) and nitric oxide metabolite (NOx) responses to the Stroop mental stress test were calculated to assess endothelial function. DefS was assessed using the Coping Strategy Indicator questionnaire. Interaction between main effects was demonstrated for 283 participants with DefS scores above the mean of 26 for L-CIMTf. RESULTS Blunted stress responses for VWF (men 16.71% vs. 51.10%; women 0.85% vs. 42.09%, respectively) and NOx (men -64.52% vs. 74.89%; women -76.16% vs. 113.29%, respectively) were evident in the DefS Blacks compared to the DefS Whites (p<0.001). ET-1 increased more in Blacks (men 150% and women 227%, p<0.001) compared to the Whites (men 61.25% and women 35.49%, p<0.001). Ambulatory pulse pressure, but not endothelial function markers, contributed to L-CIMTf (ΔR(2)=0.11 p<0.001), and L-CSWA (ΔR(2)=0.08, p<0.001) in DefS African men but not in any other group. CONCLUSIONS Blunted stress-induced NOx and VWF responses and augmented ET-1 responses in DefS Blacks indicate endothelial dysfunction. DefS may facilitate disturbed endothelial responses and enforce vascular remodelling via compensatory increases in pulse pressure in Black men. These observations may indicate an increased risk of cardiovascular incidents via functional and structural changes of the vasculature in DefS Blacks.

Directional statistics: introduction

In many of the natural and physical sciences, measurements are directions, either in two or three dimensions. The analysis of directional data relies on specific statistical models and procedures, which differ from the usual models and methodologies of Cartesian data. This chapter briefly introduces statistical models and inference for this type of data. The basic von Mises-Fisher distribution is introduced and nonparametric methods such as goodness-of-fit tests are presented. Further references are given for exploring related topics such as correlation and regression.

AN INVESTIGATION INTO THE EFFECT OF TESTOSTERONE ON THE QUANTITATIVE MAINTENANCE OF SPERMATOGENESIS IN THE HYPOPHYSECTOMIZED ADULT RAT (PHARMACOKINETICS, MORPHOMETRY, STATISTICS)

Administration of gonadotropins or testosterone (T) will maintain qualitatively normal spermatogenesis and fertility in hypophysectomized (APX) rats. However, quantitative maintenance of the spermatogenic process in APX rats treated with T alone or in combination with follicle stimulating hormone (FSH) has not been demonstrated. Studies reported here were conducted to determine whether it would be possible to increase intratesticular testosterone (ITT) levels in APX rats to those found in normal animals by administration of appropriate amounts of testosterone propionate (TP) and if under these conditions spermatogenesis can be maintained quantitatively. Quantitative analysis of spermatogenesis was performed on stages VI and VII of the spermatogenic cycle utilizing criteria of Leblond and Clermont (1952) all cell types were enumerated. In a series of experiments designed to investigate the effects of T on spermatogenesis, TP was administered to 60 day old APX rats twice daily for 30 days in doses ranging from 0.6 to 15 mg/day or from 0.6 to 6.0 mg/day in combination with FSH. The results of this study demonstrate that the efficiency of transformation of type A to type B spermatogonia and the efficacy of the meiotic prophase are related to ITT levels, and that quantitatively normal completion of the reduction division requires normal ITT levels. The ratio of spermatids to spermatocytes in the vehicle-treated APX rats was 1:1.38; in the APX rats treated with 15 mg of TP it was 1:4.0 (the theoretically expected number). This study is probably the first to demonstrate: (1) the pharmacokinetics of TP, (2) the profile and quantity of T-immunoactivity in both serum and testicular tissue of APX and IC rats as well as APX rats treated with TP alone or in combination with FSH, (3) the direct correlation of serum T and ITT levels in treated APX rats (r = 0.9, p < 0.001) as well as in the IC rats (r = 0.9, p < 0.001), (4) the significant increase in the number of Type B spermatogonia, preleptotene and pachytene spermatocytes and round spermatids in TP-treated APX rats, (5) the correlation of the number of round spermatids formed in IC rats to ITT levels (r = 0.9, p < 0.001), and (6) the correlation of the quantitative maintenance of spermatogenesis with ITT levels (r = 0.7, p < 0.001) in the testes of TP-treated APX rats. These results provide direct experimental evidence for the key role of T in the spermatogenic process. ^