Methods for controlling the type-1 error of an adaptive group sequential trial were developed in seminal papers by Cui, Hung, and Wang (Biometrics, 1999), Lehmacher and Wassmer (Biometrics, 1999), and Müller and Schäfer (Biometrics, 2001). However, corresponding solutions for the equally important and related problem of parameter estimation at the end of the adaptive trial have not been complet...

si def = jfj; xj = igj. Let s be a composition, that is to say a q-tuple which is the composition of some x in X; we set Xs = fx 2 X; s(x) = sg. We de ne and study a notion of designs for subsets of F q . In the case q = 2, our de nition coincides with the usual notion of designs and in fact our de nition is equivalent to the notion of strong colored designs of A. Bonnecaze, P. Sol e, P. Udaya ...

Craigen introduced and studied signed group Hadamard matrices extensively in [1, 2]. Livinskyi [13], following Craigen’s lead, studied and provided a better estimate for the asymptotic existence of signed group Hadamard matrices and consequently improved the asymptotic existence of Hadamard matrices. In this paper, we introduce and study signed group orthogonal designs. The main results include...