This Small Business Innovation Research Phase I project is for research on confidence intervals and hypothesis tests using fast bootstrap methods, and ways to make bootstrapping feasible for large data sets. Classical inference (intervals and tests) methods are known to be inaccurate when the underlying assumptions are violated, the usual case in practice. For example, skewness causes the usual t-test to be in error. The new methods would be an order of magnitude (power of 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 modem robust statistics, but are slow and have been little used in practice. The methods proposed are 17 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. The large sample methods would be attractive in the thriving data mining market.
