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The present contribution investigates multivariate bootstrap procedures for general stabilizing statistics, with specific application to topological data analysis.
[author] Breiman, LeoL., Meisel, WilliamW. and Purcell, EdwardE. (1977). Variable Kernel Estimates of Multivariate Densities. Technometrics 19 135–144. 10.1080/00401706.1977.10489521 \endbibitem
1977
Earlier work this paper cites.
[author] Devroye, L. P.L. P. and Wagner, T. J.T. J. (1979). The L 1 L_{1} Convergence of Kernel Density Estimates. Ann. Statist. 7 1136–1139. 536515 \endbibitem
1979
Earlier work this paper cites.
[author] Silverman, B. W.B. W. (1986). Density Estimation for Statistics and Data Analysis. Monographs on Statistics and Applied Probability. Chapman & Hall, London. 10.1007/978-1-4899-3324-9 848134 \endbibitem
1986
Earlier work this paper cites.
[author] Aldous, DavidD. and Steele, J. MichaelJ. M. (1992). Asymptotics for Euclidean Minimal Spanning Trees on Random Points. Probab. Theory Related Fields 92 247–258. 10.1007/BF01194923 1161188 \endbibitem
1992
Earlier work this paper cites.
[author] Latała, RafałR. (1997). Estimation of Moments of Sums of Independent Real Random Variables. Ann. Probab. 25 1502–1513. 10.1214/aop/1024404522 1457628 \endbibitem
1997
Earlier work this paper cites.
[author] Folland, Gerald B.G. B. (1999). Real Analysis: Modern Techniques and Applications. Wiley. \endbibitem
1999
Earlier work this paper cites.
[author] Politis, Dimitris N.D. N., Romano, Joseph P.J. P. and Wolf, MichaelM. (1999). Subsampling. Springer Series in Statistics. Springer-Verlag, New York. 10.1007/978-1-4612-1554-7 1707286 \endbibitem
1999
Earlier work this paper cites.
[author] Penrose, Mathew D.M. D. and Yukich, J. E.J. E. (2001). Central Limit Theorems for Some Graphs in Computational Geometry. Ann. Appl. Probab. 11 1005–1041. 10.1214/aoap/1015345393 1878288 \endbibitem
2001
Earlier work this paper cites.
[author] Edelsbrunner, Letscher and Zomorodian (2002). Topological Persistence and Simplification. Discrete & Computational Geometry 28 511–533. 10.1007/s00454-002-2885-2 \endbibitem
2002
Earlier work this paper cites.
[author] Penrose, Mathew D.M. D. and Yukich, J. E.J. E. (2003). Weak Laws of Large Numbers in Geometric Probability. Ann. Appl. Probab. 13 277–303. 10.1214/aoap/1042765669 1952000 \endbibitem
2003
Earlier work this paper cites.
2005
Earlier work this paper cites.
[author] Bubenik, PeterP. and Kim, Peter T.P. T. (2007). A Statistical Approach to Persistent Homology. Homology Homotopy Appl. 9 337–362. 2366953 \endbibitem
2007
Earlier work this paper cites.
[author] Hansen, Bruce E.B. E. (2008). Uniform Convergence Rates for Kernel Estimation with Dependent Data. Econometric Theory 24 726–748. 10.1017/S0266466608080304 2409261 \endbibitem
2008
Earlier work this paper cites.
[author] DeWoskin, D.D., Climent, J.J., Cruz-White, I.I., Vazquez, M.M., Park, C.C. and Arsuaga, J.J. (2010). Applications of Computational Homology to the Analysis of Treatment Response in Breast Cancer Patients. Topology Appl. 157 157–164. 10.1016/j.topol.2009.04.036 2556091 \endbibitem
2009
Earlier work this paper cites.
[author] Ferdosi, B. J.B. J., Buddelmeijer, H.H., Trager, S. C.S. C., Wilkinson, M. H. F.M. H. F. and Roerdink, J. B. T. M.J. B. T. M. (2011). Comparison of Density Estimation Methods for Astronomical Datasets. Astronomy & Astrophysics 531 A114. 10.1051/0004-6361/201116878 \endbibitem
2011
Earlier work this paper cites.
[author] Chazal, F.F., Fasy, B. T.B. T., Lecci, F.F., Rinaldo, A.A., Singh, A.A. and Wasserman, L.L. (2015). On the Bootstrap for Persistence Diagrams and Landscapes. Modeling and Analysis of Information Systems 20 111–120. 10.18255/1818-1015-2013-6-111-120 \endbibitem
2013
Earlier work this paper cites.
[author] Kramar, M.M., Goullet, A.A., Kondic, L.L. and Mischaikow, K.K. (2013). Persistence of Force Networks in Compressed Granular Media. Physical Review E 87. 10.1103/physreve.87.042207 \endbibitem
2013
Earlier work this paper cites.
[author] Fasy, Brittany TereseB. T., Lecci, FabrizioF., Rinaldo, AlessandroA., Wasserman, LarryL., Balakrishnan, SivaramanS. and Singh, AartiA. (2014). Confidence Sets for Persistence Diagrams. Ann. Statist. 42 2301–2339. 10.1214/14-AOS1252 3269981 \endbibitem
2014
Earlier work this paper cites.
[author] Turner, KatharineK., Mukherjee, SayanS. and Boyer, Doug M.D. M. (2014). Persistent Homology Transform for Modeling Shapes and Surfaces. Inf. Inference 3 310–344. 10.1093/imaiai/iau011 3311455 \endbibitem
2014
Earlier work this paper cites.
[author] Xia, KelinK., Feng, XinX., Tong, YiyingY. and Wei, Guo WeiG. W. (2014). Persistent Homology for the Quantitative Prediction of Fullerene Stability. Journal of Computational Chemistry 36 408–422. 10.1002/jcc.23816 \endbibitem
2014
Cited alongside, same era.
[author] Arsuaga, JavierJ., Borrman, TylerT., Cavalcante, RaymondR., Gonzalez, GeorginaG. and Park, CatherineC. (2015). Identification of Copy Number Aberrations in Breast Cancer Subtypes Using Persistence Topology. Microarrays 4 339–369. 10.3390/microarrays4030339 \endbibitem
2015
Cited alongside, same era.
[author] Bobrowski, OmerO. and Mukherjee, SayanS. (2015). The Topology of Probability Distributions on Manifolds. Probab. Theory Related Fields 161 651–686. 10.1007/s00440-014-0556-x 3334278 \endbibitem
2015
Cited alongside, same era.
[author] Bubenik, PeterP. (2015). Statistical Topological Data Analysis Using Persistence Landscapes. J. Mach. Learn. Res. 16 77–102. 3317230 \endbibitem
2015
Cited alongside, same era.
[author] Chazal, FrédéricF. and Divol, VincentV. (2018). The Density of Expected Persistence Diagrams and Its Kernel Based Estimation. In 34th International Symposium on Computational Geometry. LIPIcs. Leibniz Int. Proc. Inform. 99 Art. No. 26, 15. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern. 3824270 \endbibitem
2018
Later among the works it cites.
[author] Hiraoka, YasuakiY., Shirai, TomoyukiT. and Trinh, Khanh DuyK. D. (2018). Limit Theorems for Persistence Diagrams. Ann. Appl. Probab. 28 2740–2780. 10.1214/17-AAP1371 3847972 \endbibitem
2018
Later among the works it cites.
[author] Kim, JisuJ., Shin, JaehyeokJ., Rinaldo, AlessandroA. and Wasserman, LarryL. (2018). Uniform Convergence Rate of the Kernel Density Estimator Adaptive to Intrinsic Volume Dimension. \endbibitem
2018
Later among the works it cites.
[author] Owada, TakashiT. (2018). Limit Theorems for Betti Numbers of Extreme Sample Clouds with Application to Persistence Barcodes. Ann. Appl. Probab. 28 2814–2854. 10.1214/17-AAP1375 3847974 \endbibitem
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[author] Chazal, FrédéricF., Fasy, Brittany TereseB. T., Lecci, FabrizioF., Rinaldo, AlessandroA. and Wasserman, LarryL. (2015). Stochastic Convergence of Persistence Landscapes and Silhouettes. J. Comput. Geom. 6 140–161. 3323391 \endbibitem
2015
Cited alongside, same era.
[author] Chen, Yen-ChiY.-C., Wang, DarenD., Rinaldo, AlessandroA. and Wasserman, LarryL. (2015). Statistical Analysis of Persistence Intensity Functions. \endbibitem
2015
Cited alongside, same era.
[author] Last, GünterG., Peccati, GiovanniG. and Schulte, MatthiasM. (2015). Normal Approximation on Poisson Spaces: Mehler’s Formula, Second Order Poincaré Inequalities and Stabilization. Probability Theory and Related Fields 165 667–723. 10.1007/s00440-015-0643-7 \endbibitem
2015
Cited alongside, same era.
[author] Yogeshwaran, D.D. and Adler, Robert J.R. J. (2015). On the Topology of Random Complexes Built Over Stationary Point Processes. Ann. Appl. Probab. 25 3338–3380. 10.1214/14-AAP1075 3404638 \endbibitem
2015
Cited alongside, same era.
[author] Camara, Pablo G.P. G., Rosenbloom, Daniel I. S.D. I. S., Emmett, Kevin J.K. J., Levine, Arnold J.A. J. and Rabadan, RaulR. (2016). Topological Data Analysis Generates High-Resolution, Genome-wide Maps of Human Recombination. Cell Systems 3 83–94. 10.1016/j.cels.2016.05.008 \endbibitem
2016
Cited alongside, same era.
[author] Kramár, MiroslavM., Levanger, RachelR., Tithof, JeffreyJ., Suri, BalachandraB., Xu, MuM., Paul, MarkM., Schatz, Michael F.M. F. and Mischaikow, KonstantinK. (2016). Analysis of Kolmogorov Flow and Rayleigh–bénard Convection Using Persistent Homology. Physica D: Nonlinear Phenomena 334 82–98. 10.1016/j.physd.2016.02.003 \endbibitem
2016
Cited alongside, same era.
[author] Pranav, PratyushP., Edelsbrunner, HerbertH., van de Weygaert, RienR., Vegter, GertG., Kerber, MichaelM., Jones, Bernard J. T.B. J. T. and Wintraecken, MathijsM. (2016). The Topology of the Cosmic Web in Terms of Persistent Betti Numbers. Monthly Notices of the Royal Astronomical Society 465 4281–4310. 10.1093/mnras/stw2862 \endbibitem
2016
Cited alongside, same era.
[author] Singh, ShashankS. and Póczos, BarnabásB. (2016). Analysis of k-Nearest Neighbor Distances with Application to Entropy Estimation. \endbibitem
2016
Cited alongside, same era.
2018
Later among the works it cites.
[author] Wasserman, LarryL. (2018). Topological Data Analysis. Annu. Rev. Stat. Appl. 5 501–535. 10.1146/annurev-statistics-031017-100045 3774757 \endbibitem
2018
Later among the works it cites.
[author] Chung, Yu-MinY.-M. and Lawson, AustinA. (2019). Persistence Curves: A Canonical Framework for Summarizing Persistence Diagrams. \endbibitem
2019
Later among the works it cites.
[author] Crawford, LorinL., Monod, AntheaA., Chen, Andrew X.A. X., Mukherjee, SayanS. and Rabadán, RaúlR. (2019). Predicting Clinical Outcomes in Glioblastoma: An Application of Topological and Functional Data Analysis. Journal of the American Statistical Association 1–12. 10.1080/01621459.2019.1671198 \endbibitem
2019
Later among the works it cites.
[author] Krebs, Johannes T. N.J. T. N. and Polonik, WolfgangW. (2019). On the Asymptotic Normality of Persistent Betti Numbers. \endbibitem
2019
Later among the works it cites.
[author] Lachièze-Rey, RaphaëlR., Schulte, MatthiasM. and Yukich, J. E.J. E. (2019). Normal Approximation for Stabilizing Functionals. The Annals of Applied Probability 29. 10.1214/18-aap1405 \endbibitem
2019
Later among the works it cites.
[author] Pranav, PratyushP., Adler, Robert J.R. J., Buchert, ThomasT., Edelsbrunner, HerbertH., Jones, Bernard J. T.B. J. T., Schwartzman, ArminA., Wagner, HubertH. and van de Weygaert, RienR. (2019). Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background. Astronomy & Astrophysics 627 A163. 10.1051/0004-6361/201834916 \endbibitem
2019
Later among the works it cites.
[author] Pranav, PratyushP., van de Weygaert, RienR., Vegter, GertG., Jones, Bernard J TB. J. T., Adler, Robert JR. J., Feldbrugge, JobJ., Park, ChangbomC., Buchert, ThomasT. and Kerber, MichaelM. (2019). Topology and Geometry of Gaussian Random Fields I: On Betti Numbers, Euler Characteristic, and Minkowski Functionals. Monthly Notices of the Royal Astronomical Society 485 4167–4208. 10.1093/mnras/stz541 \endbibitem
2019
Later among the works it cites.
[author] Trinh, Khanh DuyK. D. (2019). On Central Limit Theorems in Stochastic Geometry for Add-one Cost Stabilizing Functionals. Electron. Commun. Probab. 24 Paper No. 76, 15. 10.1214/19-ecp279 4049088 \endbibitem
2019
Later among the works it cites.
[author] Ulmer, M.M., Ziegelmeier, LoriL. and Topaz, Chad M.C. M. (2019). A Topological Approach to Selecting Models of Biological Experiments. PLOS ONE 14 1-18. 10.1371/journal.pone.0213679 \endbibitem
2019
Later among the works it cites.
[author] Biscio, Christophe A. N.C. A. N., Chenavier, NicolasN., Hirsch, ChristianC. and Svane, Anne MarieA. M. (2020). Testing Goodness of Fit for Point Processes Via Topological Data Analysis. Electron. J. Stat. 14 1024–1074. 10.1214/20-EJS1683 4067816 \endbibitem
2020
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[author] Lachièze-Rey, RaphaëlR., Peccati, GiovanniG. and Yang, XiaochuanX. (2020). Quantitative Two-scale Stabilization on the Poisson Space. \endbibitem
2020
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[author] Roycraft, BenjaminB. (2021). github.com/btroycraft/stabilizing_statistics_bootstrap. 10.5281/ZENODO.4627098 \endbibitem
2021
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[author] Roycraft, BenjaminB., Krebs, JohannesJ. and Polonik, WolfgangW. (2021). Supplement to ”Bootstrapping Persistent Betti Numbers and Other Stabilizing Statistics”. \endbibitem
2021
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[author] Owada, TakashiT. and Adler, Robert J.R. J. (2017). Limit Theorems for Point Processes under Geometric Constraints (and Topological Crackle). Ann. Probab. 45 2004–2055. 10.1214/16-AOP1106 3650420 \endbibitem
2055
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