Quasi-random resampling for the bootstrap Export

@article{citeulike:1708041, abstract = {Quasi-random sequences are known to give efficient numerical integration rules in many Bayesian statistical problems where the posterior distribution can be transformed into periodic functions on then-dimensional hypercube. From this idea we develop a quasi-random approach to the generation of resamples used for Monte Carlo approximations to bootstrap estimates of bias, variance and distribution functions. We demonstrate a major difference between quasi-random bootstrap resamples, which are generated by deterministic algorithms and have no true randomness, and the usual pseudo-random bootstrap resamples generated by the classical bootstrap approach. Various quasi-random approaches are considered and are shown via a simulation study to result in approximants that are competitive in terms of efficiency when compared with other bootstrap Monte Carlo procedures such as balanced and antithetic resampling.}, author = {Do, Kim-Anh and Hall, Peter}, citeulike-article-id = {1708041}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/BF01890833}, day = {1}, doi = {10.1007/BF01890833}, journal = {Statistics and Computing}, keywords = {asymptotics, balanced\_bootstrap, bootstrap, quasi\_monte\_carlo}, number = {1}, pages = {13--22}, posted-at = {2007-09-29 14:57:23}, priority = {0}, title = {Quasi-random resampling for the bootstrap}, url = {http://dx.doi.org/10.1007/BF01890833}, volume = {1}, year = {1991} }

TY - JOUR ID - citeulike:1708041 L3 - citeulike-article-id:1708041 N2 - Quasi-random sequences are known to give efficient numerical integration rules in many Bayesian statistical problems where the posterior distribution can be transformed into periodic functions on then-dimensional hypercube. From this idea we develop a quasi-random approach to the generation of resamples used for Monte Carlo approximations to bootstrap estimates of bias, variance and distribution functions. We demonstrate a major difference between quasi-random bootstrap resamples, which are generated by deterministic algorithms and have no true randomness, and the usual pseudo-random bootstrap resamples generated by the classical bootstrap approach. Various quasi-random approaches are considered and are shown via a simulation study to result in approximants that are competitive in terms of efficiency when compared with other bootstrap Monte Carlo procedures such as balanced and antithetic resampling. IS - 1 JF - Statistics and Computing EP - 22 TI - Quasi-random resampling for the bootstrap VL - 1 SP - 13 KW - asymptotics KW - balanced_bootstrap KW - bootstrap KW - quasi_monte_carlo AU - Do, Kim-Anh AU - Hall, Peter PY - 1991//01/ UR - http://dx.doi.org/10.1007/BF01890833 ER -