SBIR Phase II: Bootstrap Tilting Inference and Large Data Sets

这个小型企业创新研究第二阶段项目是为了开发快速自举可信区间和假设检验，以及使自举适用于大型数据集的方法。众所周知，当违反理论假设时，经典的推理(区间和测试)方法是不准确的，这在实践中是常见的情况。例如，偏度会导致通常的t检验出错。新方法通常比经典推论准确一个数量级(SQRT(N)的幂，其中n是样本大小)。Bootstrap方法是一种很有前途的经典推理方法，可以处理包括现代稳健统计在内的复杂统计，但速度慢，在实践中应用很少，所提出的方法通常比其他Bootstrap方法快17-37倍。这些方法速度足够快，可以无缝地整合到标准软件中，与经典推理并驾齐驱，或者取而代之。这为统计从业者提供了一个现实的选择，以取代简单但不准确的经典推断和非稳健的方法。最先做到这一点的公司的竞争优势是一个重大机遇。此外，在蓬勃发展的数据挖掘市场中，大样本方法将具有吸引力。

This Small Business Innovation Research Phase II project is for development of fast bootstrap confidence intervals and hypothesis tests, and ways to make bootstrapping feasible for large data sets. Classical inference (intervals and tests) methods are known to be inaccurate when theoretical assumptions are violated, the usual case in practice. For example, skewness causes the usual t-test to be in error. The new methods are an order of magnitude (power of sqrt(n), where n is the sample size) more accurate in general than classical inferences. Bootstrap methods are a promising alternative to classical inferences, and can handle complex statistics including modern robust statistics, but are slow and have been little used in practice.The methods proposed are typically 17--37 times faster than other bootstrap methods. The methods are fast enough to be seamlessly incorporated into standard software, alongside or instead of classical inferences. This provides statistical practitioners a realistic alternative to easy but inaccurate classical inferences and non-robust methods. The competitive advantage to the firm that does this first is a major opportunity. Furthermore, the large sample methods would be attractive in the thriving data mining market.