TY - JOUR
AU - Shasha Wang
AU - Wen-Qing Xu
AU - Jitao Liu
PY - 2021/03/28
Y2 - 2021/04/15
TI - Random Polygons and Optimal Extrapolation Estimates of pi
JF - Statistics, Optimization & Information Computing
JA - Stat., optim. inf. comput.
VL - 9
IS - 1
SE - Research Articles
DO - 10.19139/soic-2310-5070-1193
UR - http://iapress.org/index.php/soic/article/view/1193
AB - We construct optimal extrapolation estimates of π based on random polygons generated by n independent points uniformly distributed on a unit circle in R2. While the semiperimeters and areas of these random n-gons converge to π almost surely and are asymptotically normal as n → ∞, in this paper we develop various extrapolation processes to further accelerate such convergence. By simultaneously considering the random n-gons and suitably constructed random 2n-gons and then optimizing over functionals of the semiperimeters and areas of these random polygons, we derive several new estimates of π with faster convergence rates. These extrapolation improvements are also shown to be asymptotically normal as n → ∞.
ER -