The hazard rate is a statistical indicator commonly used in lifetime analysis. The Birnbaum-Saunders (BS) model is a life distribution originated from a problem pertaining to material fatigue that has been applied to diverse fields. The BS model relates the total time until failure to some type of cumulative damage that is normally distributed. The generalized BS (GBS) distribution is a class o...

In least squares, least absolute deviations, and even generalized M-estimation, outlying observations sometimes strongly influence the estimation result, masking an important and interesting relationship existing in the majority of observations. The S-estimators are a class of estimators that overcome this difficulty by smoothly downweighting outliers in fitting regression functions to data. In...

Allowing for gene-environment correlation, Jensen (1975) reports that under a wide range of assumptions, the twin data show that onehalf ~o th~ee-fourths of IQ variance is accounted for by genetic factors. But that conc1usion;~fa11swhen an arbitrary specification is relaxed. ON JENSEN'S METHOD FOR TWINS

A general class of Newton algorithms on Graßmann and Lagrange–Graßmann manifolds is introduced, that depends on an arbitrary pair of local coordinates. Local ⋆ corresponding author The first author was partially supported by a grant from BMBF within the FprofUnd programme. The second and third author are with National ICT Australia Limited which is funded by the Australian Government’s Departme...

Let C[[z]] be the ring of power series over an effective ring C. In [BK78], it was first shown that differential equations over C[[z]] may be solved in an asymptotically efficient way using Newton’s method. More precisely, if M(n) denotes the complexity in order two polynomials of degree < n over C, then the first n coefficients of the solution can be computed in time O(M(n)). However, this com...

On modern large-scale parallel computers, the performance of Krylov subspace iterative methods is limited by global synchronization. This has inspired the development of s-step (or communication-avoiding) Krylov subspace method variants, in which iterations are computed in blocks of s. This reformulation can reduce the number of global synchronizations per iteration by a factor of O(s), and has...

I L L U S T R A T I O N B Y M A T T H E W C O O P E R THE PROGRAM TERMINATION problem, also known as the uniform halting problem, can be defined as follows: Using only a finite amount of time, determine whether a given program will always finish running or could execute forever. This problem rose to prominence before the invention of the modern computer, in the era of Hilbert’s Entscheidungspro...