Resumen
Under a very general setting, we consider the problem of estimating a linear functional of an unknown vector in a Hilbert space from indirect data contaminated by noise. We then discuss two situations in detail: estimating the signal function in the fractional Brownian motion model and the regression model with correlated errors. In the fractional Brownian motion model, we observe the process which is the sum of a fractional Brownian motion with Hurst index between View the MathML source and a drift function that is determined by the signal function. In the regression model with correlated errors, we assume that the errors have long memory. For both estimation problems, we obtain the asymptotic rate for the minimax affine risks over certain types of parameter spaces. In each case, we also show that the minimax affine risk is bounded by 1.25 times the minimax risk.

Resumen
For the competing risk setting where the lifetime data are due to one of several distinct and exclusive causes, comparison of cause-specific hazard rates is of interest to researchers. In this paper we survey existing methods for related tests and provide a new test for a common overall rate for all causes and groups. Tests given in the literature for checking for a common rate for causes and a common rate for the groups are shown to be in the same framework as the proposed test for common overall rate. Asymptotics are shown to follow a common theme for each test. An extensive numerical and graphical investigation and an example are presented to substantiate the proposed methods.