@article{Wang_Xu_Liu_2021, title={Random Polygons and Optimal Extrapolation Estimates of pi}, volume={9}, url={http://iapress.org/index.php/soic/article/view/1193}, DOI={10.19139/soic-2310-5070-1193}, abstractNote={<p>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 → ∞.</p>}, number={1}, journal={Statistics, Optimization & Information Computing}, author={Wang, Shasha and Xu, Wen-Qing and Liu, Jitao}, year={2021}, month={Mar.}, pages={241-249} }