Accurate approximation to sampling distributions

我的目标是开发各种统计模型的抽样分布的精确近似值，这将适用于任何实际大小的样本（在许多情况下，通常的正态近似值仅适用于不切实际的大样本）。这是通过将这些分布以样本量的反幂展开，并找到这种展开的前几项来完成的。该技术需要大量的符号计算和相应的程序开发。这些结果用于为这些模型的未知参数值构造准确的置信区间，这是统计学的主要任务之一。该项目还将涉及对这些扩展的收敛性进行更多的理论研究。

I aim to develop accurate approximations to sampling distributions of various statistical models, which would be applicable to samples of any practical size (in many cases, the usual Normal approximation works well only with unrealistically large samples). This is done by expanding these distributions in inverse powers of the sample size, and finding the first few terms of such expansions. The technique requires large amount of symbolic computation, and the corresponding program development. The results are used for constructing accurate confidence intervals for values of unknown parameters of these models, which is one of the primary tasks of Statistics. The project will also involve a more theoretical study of convergence of these expansions.