A new estimator of the essential parameter theta = 4Ne mu from DNA polymorphism data is developed under the neutral Wright-Fisher model without recombination and population subdivision, where Ne is the effective population size and mu is the mutation rate per locus per generation. The new estimator has a variance only slightly larger than the minimum variance of all possible unbiased estimators...

Evaluating the performance of an agent or group of agents can be, by itself, a very challenging problem. The stochastic nature of the environment plus the stochastic nature of agents’ decisions can result in estimates with intractably large variances. This paper examines the problem of finding low variance estimates of agent performance. In particular, we assume that some agent-environment dyna...

From the title, one might assume that issues raised in this article must have been settled long ago. In a sense this is true. This may be one of those cases of failed communication between mathematicians and physicists, experimental physicists in particular. In the Introduction we show that a common approach to this linear, single-parameter estimation problem converges to the minimum variance, ...

Using higher-order derivative with respect to the parameter, we will give lower bounds for variance of unbiased estimators in quantum estimation problems. This is a quantum version of the Bhattacharyya inequality in the classical statistical estimation. Because of non-commutativity of operator multiplication, we obtain three different types of lower bounds; Type S, Type R and Type L. If the par...