Bootstrapping r fold Tensor Data, Art Owen, Stanford University скачать в хорошем качестве

Bootstrapping r fold Tensor Data, Art Owen, Stanford University

The famous Netflix data is a sparsely sampled table with rows for customers and columns for movies (or vice versa). Both movies and rows are naturally modeled as random ef-fects. Bootstrapping such data is problematic: no proper bootstrap can exist, according to a theorem of Peter Mc-Cullagh. Resampling rows and columns independently is effective though slightly conservative. Computerized data gathering frequently produces data sets with three-way or even higher order data tables. We present a bootstrap for such tensor valued data. Our version uses independent weights instead of multinomial ones. It remains mildly conservative. Poisson weights are close to the original bootstrap, but binary weights have computational and sta-tistical advantages. Under certain conditions a single boot-strap replicate suffices to give a variance estimate. We apply our method to compare the length of comments made by Facebook users in the US and the UK. This work is joint with Dean Eckles, Facebook.