Q: Consider an uncorrelated (white) Gaussian signal s(t). Calculate its 3rd and 4th order moments, m3 = ⟨s(t1)s(t2)s(t3)⟩ and m4 = ⟨s(t1)s(t2)s(t3)s(t4)⟩. Confirm with simulation. The third moment m3 = ⟨s(t1)s(t2)s(t3)⟩ is zero. Namely, if t1 ̸= t2 ̸= t3 then m3 = ⟨s⟩ = 03 = 0. If t1 = t2 = t3, m3 = ⟨ s3 ⟩ = ́ N (0, σ2)x3dx = 0, as this is the integral over an odd function. For t1 = t2 ̸= t3, m3 = ...

Background T2 is sensitive to hemoglobin oxygen saturation (%HbO2). Non-invasive, rapid in-vivo quantification of %HbO2 based on the T2 of blood may be useful in patients with congenital heart disease. Although singleshot, T2-prepared SSFP enables rapid myocardial T2 quantification [1], flow sensitivity of the T2 preparation, especially at later echo times, may cause an underestimation of T2 va...

Inspired by the cross-ratio proposed Clayton, we study a new risk ratio to describe relation between components of random vector (T1,T2). It is conditional hazard rate function T1 at t1, given that T2≥t2 and T2<t2. A nonparametric estimator its asymptotic distribution obtained using Bernstein smoothing for survival copula (T1,T2) derivatives. The finite sample performance studied via simulation...