Compound estimation of a monotone sequence

In this paper we consider simultaneous estimation of a monotone sequence of parameters in the context of compound decision theory and obtain a class of monotone estimators with the strong asymptotic property that their compound risk converges uniformly to zero, for a large class of loss functions including the square error loss function and the absolute deviation loss function, as the number of parameters increases. We also show that when the number of parameters is fixed our estimators converge uniformly in probability to the parameters they are estimating, as the number of observations increases. As examples we consider estimation of forces of mortality with censored data in single and double decrement environments.