Consider both the classical and some more general invariant decision problems of estimating a continuous distribution function, with the loss function L ( F , a ) = f ( F ( t ) a(t))2h(F(t))dF(t) and a sample of size n from F. It is proved that any nonrandomized estimator can be approximated in Lebesgue measure by the more general invariant estimators. Some methods for investigating the finite ...

     The quadratic loss function has been used by decision-theoretic statisticians and economists for many years.  In this paper  the estimation of scale parameter under a bounded loss function, which is adequate for assessing quality and quality improvement, is considered with restriction to the principles of invariance and risk unbiasedness. An implicit form of minimum risk scale equivariant ...

The moment’s estimator (Dekkers et al., 1989) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The location invariant Hill-type estimator (Fraga Alves, 2001) is only suitable to estimate positive indices. In this paper, a new moment-type estimator is studied, which is location invariant. This new estimator is based on the original moment-type e...

Hall and Welsh (1984) established the best attainable rate of convergence for estimates of a positive extreme value index under a certain second order condition implying that the distribution function of the maximum of n random variables converges at an algebraic rate to the pertaining extreme value distribution. As a rst generalization we obtain a surprisingly sharp bound on the estimation err...

Via a unified view of probability estimation, classification, and prediction, we derive a uniformlyoptimal combined-probability estimator, construct a classifier that uniformly approaches the error of the best possible label-invariant classifier, and improve existing results on pattern prediction and compression. ∗[email protected] †[email protected] ‡[email protected] §[email protected]