Family studies are a useful alternative to twin studies for disentangling genetic and environmental effects on human diseases. However, although age-at-onset traits are often of interest, family-based quantitative genetic analysis of such data is still not commonly used. One reason is that we need multiple random components to capture the genetic and environmental contributions, so it becomes h...

We derive the asymptotic distributions of a semiparametric Dikta-type estimator and an inverse probability weighted type estimator of a survival function for a missing censoring indicator left truncated model and provide a theoretical comparison study.

We analyze an augmented inverse probability of non-missingness weighted estimator of a survival function for a missing censoring indicator model, in the absence and presence of left truncation. The estimator improves upon its precursor but is still not the best in terms of achieving minimal asymptotic variance.

Suppose an estimator sequence Tn. is asymptotically efficient for a. • smooth functional 1'1;. Then a Hadamard differentia.ble functional rf> applied to Tn is efficient for i f> 0 11':. More generally, Hadamard dif-ferentiability ma.y be used to esta.blish asymptotic efficiency. Three non-trivial applications are discussed: random right censoring, random truncation and estima.ting a. point symm...

986812401 Doubly truncated data appear in a number of applications, including astronomy and survival analysis. In this paper we review the existing methods to compute the NPMLE under double truncation, which has no explicit form and must be approximated numerically. We introduce the bootstrap as a method to estimate the finite sample distribution of the NPMLE under double truncation. The perfor...

Every word $w$ in a free group naturally induces probability measure on every compact $G$. For example, if $w=\left[x,y\right]$ is the commutator word, random element sampled by $w$-measure given $\left[g,h\right]$ of two independent, Haar-random elements Back 1896, Frobenius showed that $G$ finite and $\psi$ an irreducible character, then expected value $\psi\left(\left[g,h\right]\right)$ $\fr...

Background: Conventional echocardiography and tissue Doppler imaging have been highlighted to diagnose diastolic and systolic heart dysfunction. We aimed to compare tissue Doppler imaging with conventional echocardiography to diagnose heart dysfunctions in diabetes mellitus type 1 (DMT1) patients. <s...