Bootstrapping multivariate UU-quantiles and related statistics

AbstractThe asymptotic consistency of the bootstrap approximation of the vector of the marginal generalized quantiles of U-statistic structure (multivariate U-quantiles for short) is established. The asymptotic accuracy of the bootstrap approximation is also obtained. Extensions to smooth functions of marginal generalized quantiles are given and some specific examples, such as the vector of marginal sample quantiles and the vector of marginal Hodges-Lehmann location estimators, are discussed

On a crossroad of resampling plans : bootstrapping elementary symmetric polynomials

We investigate the validity of the bootstrap method for the elementary symmetric polynomials S_n^{(k)={nchoose k^{-1sumsb {1leq i_1 < ...< i_k leq n X_{i_1...X_{i_k of i.i.d. random variables $X_1,dots,X_n$. For both fixed and increasing order $k$, as $ntoinfty$ the cases where mu= {rm E X_1 neq0, the nondegenerate case, and where mu= {rm E X_1=0, the degenerate case, are considered

Epoxyeicosatrienoic Acid-Based Therapy Attenuates the Progression of Postischemic Heart Failure in Normotensive Sprague-Dawley but Not in Hypertensive Ren-2 Transgenic Rats

Epoxyeicosatrienoic acids (EETs) and their analogs have been identified as potent antihypertensive compounds with cardio- and renoprotective actions. Here, we examined the effect of EET-A, an orally active EET analog, and c-AUCB, an inhibitor of the EETs degrading enzyme soluble epoxide hydrolase, on the progression of post-myocardial infarction (MI) heart failure (HF) in normotensive Hannover Sprague-Dawley (HanSD) and in heterozygous Ren-2 transgenic rats (TGR) with angiotensin II-dependent hypertension. Adult male rats (12 weeks old) were subjected to 60-min left anterior descending (LAD) coronary artery occlusion or sham (non-MI) operation. Animals were treated with EET-A and c-AUCB (10 and 1 mg/kg/day, respectively) in drinking water, given alone or combined for 5 weeks starting 24 h after MI induction. Left ventricle (LV) function and geometry were assessed by echocardiography before MI and during the progression of HF. At the end of the study, LV function was determined by catheterization and tissue samples were collected. Ischemic mortality due to the incidence of sustained ventricular fibrillation was significantly higher in TGR than in HanSD rats (35.4 and 17.7%, respectively). MI-induced HF markedly increased LV end-diastolic pressure (Ped) and reduced fractional shortening (FS) and the peak rate of pressure development [+(dP/dt)max] in untreated HanSD compared to sham (non-MI) group [Ped: 30.5 ± 3.3 vs. 9.7 ± 1.3 mmHg; FS: 11.1 ± 1.0 vs. 40.8 ± 0.5%; +(dP/dt)max: 3890 ± 291 vs. 5947 ± 309 mmHg/s]. EET-A and c-AUCB, given alone, tended to improve LV function parameters in HanSD rats. Their combination amplified the cardioprotective effect of single therapy and reached significant differences compared to untreated HanSD controls [Ped: 19.4 ± 2.2 mmHg; FS: 14.9 ± 1.0%; +(dP/dt)max: 5278 ± 255 mmHg/s]. In TGR, MI resulted in the impairment of LV function like HanSD rats. All treatments reduced the increased level of albuminuria in TGR compared to untreated MI group, but neither single nor combined EET-based therapy improved LV function. Our results indicate that EET-based therapy attenuates the progression of post-MI HF in HanSD, but not in TGR, even though they exhibited renoprotective action in TGR hypertensive rats

On a Crossroad of Resampling Plans: Bootstrapping Elementary Symmetric Polynomials

We investigate the validity of the bootstrap method for the elementary symmetric polynomials S (k) n = i n k j \Gamma1 P 1i 1 !:::!i k n X i 1 :::X i k of i.i.d. random variables X 1 ; : : : ; X n . For both fixed and increasing order k, as n !1 the cases where = EX 1 6= 0, the nondegenerate case, and where = EX 1 = 0, the degenerate case, are considered. 1991 Mathematics Subject Classification: 62G09, 62E20, 60F05. Keywords and Phrases: bootstrapping, elementary symmetric polynomials. Note: Work carried out under project PNA 3.2 &quot;Statistics&quot;. 1 Introduction Let X 1 ; : : : ; X n be independent and identically distributed random variables with common distribution function F and \Gamma1 ! = EX 1 ! 1; 0 ! oe 2 = oe 2 (X 1 ) ! 1: (1) Partially supported by grant GAUK 365 of Charles University Prague, and the focus area &quot;Computationally Intensive Methods in Stochastics&quot; of the Netherlands Organization for Scientific Research (NWO). 1 Let, for any 1 k n, S (k) n ..

Two pharmacological epoxyeicosatrienoic acid-enhancing therapies are effectively antihypertensive and reduce the severity of ischemic arrhythmias in rats with angiotensin II-dependent hypertension.

ObjectiveWe examined the effects of treatment with soluble epoxide hydrolase inhibitor (sEHi) and epoxyeicosatrienoic acids (EETs) analogue (EET-A), given alone or combined, on blood pressure (BP) and ischemia/reperfusion myocardial injury in rats with angiotensin II (ANG II)-dependent hypertension.MethodsRen-2 transgenic rats (TGR) were used as a model of ANG II-dependent hypertension and Hannover Sprague-Dawley rats served as controls. Rats were treated for 14 days with sEHi or EET-A and BP was measured by radiotelemetry. Albuminuria, cardiac hypertrophy and concentrations of ANG II and EETs were determined. Separate groups were subjected to acute myocardial ischemia/reperfusion injury and the infarct size and ventricular arrhythmias were determined.ResultsTreatment of TGR with sEHi and EET-A, given alone or combined, decreased BP to a similar degree, reduced albuminuria and cardiac hypertrophy to similar extent; only treatment regimens including sEHi increased myocardial and renal tissue concentrations of EETs. sEHi and EET-A, given alone or combined, suppressed kidney ANG II levels in TGR. Remarkably, infarct size did not significantly differ between TGR and Hannover Sprague-Dawley rats, but the incidence of ischemia-induced ventricular fibrillations was higher in TGR. Application of sEHi and EET-A given alone and combined sEHi and EET-A treatment were all equally effective in reducing life-threatening ventricular fibrillation in TGR.ConclusionThe findings indicate that chronic treatment with either sEHi or EET-A exerts distinct antihypertensive and antiarrhythmic actions in our ANG II-dependent model of hypertension whereas combined administration of sEHi and EET-A does not provide additive antihypertensive or cardioprotective effects

Epoxyeicosatrienoic Acid-Based Therapy Attenuates the Progression of Postischemic Heart Failure in Normotensive Sprague-Dawley but Not in Hypertensive Ren-2 Transgenic Rats.

Epoxyeicosatrienoic acids (EETs) and their analogs have been identified as potent antihypertensive compounds with cardio- and renoprotective actions. Here, we examined the effect of EET-A, an orally active EET analog, and c-AUCB, an inhibitor of the EETs degrading enzyme soluble epoxide hydrolase, on the progression of post-myocardial infarction (MI) heart failure (HF) in normotensive Hannover Sprague-Dawley (HanSD) and in heterozygous Ren-2 transgenic rats (TGR) with angiotensin II-dependent hypertension. Adult male rats (12 weeks old) were subjected to 60-min left anterior descending (LAD) coronary artery occlusion or sham (non-MI) operation. Animals were treated with EET-A and c-AUCB (10 and 1 mg/kg/day, respectively) in drinking water, given alone or combined for 5 weeks starting 24 h after MI induction. Left ventricle (LV) function and geometry were assessed by echocardiography before MI and during the progression of HF. At the end of the study, LV function was determined by catheterization and tissue samples were collected. Ischemic mortality due to the incidence of sustained ventricular fibrillation was significantly higher in TGR than in HanSD rats (35.4 and 17.7%, respectively). MI-induced HF markedly increased LV end-diastolic pressure (Ped) and reduced fractional shortening (FS) and the peak rate of pressure development [+(dP/dt)max] in untreated HanSD compared to sham (non-MI) group [Ped: 30.5 ± 3.3 vs. 9.7 ± 1.3 mmHg; FS: 11.1 ± 1.0 vs. 40.8 ± 0.5%; +(dP/dt)max: 3890 ± 291 vs. 5947 ± 309 mmHg/s]. EET-A and c-AUCB, given alone, tended to improve LV function parameters in HanSD rats. Their combination amplified the cardioprotective effect of single therapy and reached significant differences compared to untreated HanSD controls [Ped: 19.4 ± 2.2 mmHg; FS: 14.9 ± 1.0%; +(dP/dt)max: 5278 ± 255 mmHg/s]. In TGR, MI resulted in the impairment of LV function like HanSD rats. All treatments reduced the increased level of albuminuria in TGR compared to untreated MI group, but neither single nor combined EET-based therapy improved LV function. Our results indicate that EET-based therapy attenuates the progression of post-MI HF in HanSD, but not in TGR, even though they exhibited renoprotective action in TGR hypertensive rats