Asymptotic properties of Turing’s formula in relative error

Asymptotic Error Estimates for the Gauss Quadrature Formula

Asymptotic Relative Efficiency in Testing

Making a substantiated choice of the most efficient statistical test of several ones being at the disposal of the statistician is regarded as one of the basic problems of Statistics. This problem became especially important in the middle of XX century when appeared computationally simple but ”inefficient” rank tests. Asymptotic relative efficiency (ARE) is a notion which enables to implement in...

Asymptotic Relative Efficiency in Estimation

For statistical estimation problems, it is typical and even desirable that several reasonable estimators can arise for consideration. For example, the mean and median parameters of a symmetric distribution coincide, and so the sample mean and the sample median become competing estimators of the point of symmetry. Which is preferred? By what criteria shall we make a choice? One natural and time-...

Asymptotic relative efficiency.

Asymptotic Relative Efficiency ] was pleased to read "Promise in Nonparametrics" by Royeen and Seaver (March, ] 986). As the authors state, analysis of data by non parametric methods when the strong assumptions for parametric counterparts cannot be met provides the researcher with effective statistical procedures that may be more realistic and valid in a given situation. It is also interesting ...

The Asymptotic Formula in Waring’s Problem

We derive a new minor arc bound, suitable for applications associated with Waring’s problem, from Vinogradov’s mean value theorem. In this way, the conjectured asymptotic formula in Waring’s problem is established for sums of s kth powers of natural numbers when k > 6 and s > 2k − 11.