-
2
-
-
84908161422
-
-
Preprint. Available at arXiv: 1112.5627
-
BALAKRISHNAN, S., RINALDO, A., SHEEHY, D., SINGH, A. and WASSERMAN, L. (2011). Mini-max rates for homology inference. Preprint. Available at arXiv:1112.5627.
-
(2011)
Mini-max Rates for Homology Inference
-
-
Balakrishnan, S.1
Rinaldo, A.2
Sheehy, D.3
Singh, A.4
Wasserman, L.5
-
3
-
-
82255180677
-
Improving homology estimates with random walks
-
MR2854318
-
BENDICH, P., GALKOVSKYI, T. and HARER, J. (2011). Improving homology estimates with random walks. Inverse Problems 27 124002. MR2854318
-
(2011)
Inverse Problems
, vol.27
, pp. 124002
-
-
Bendich, P.1
Galkovskyi, T.2
Harer, J.3
-
5
-
-
84908161421
-
-
Preprint. Available at arXiv: 1206.4581
-
BLUMBERG, A. J., GAL, I., MANDELL, M. A. and PANCIA, M. (2012). Persistent homology for metric measure spaces, and robust statistics for hypothesis testing and confidence intervals. Preprint. Available at arXiv:1206.4581.
-
(2012)
Persistent Homology for Metric Measure Spaces, and Robust Statistics for Hypothesis Testing and Confidence Intervals
-
-
Blumberg, A.J.1
Gal, I.2
Mandell, M.A.3
Pancia, M.4
-
6
-
-
37849007580
-
A statistical approach to persistent homology. Homology
-
MR2366953
-
BUBENIK, P. and KIM, P. T. (2007). A statistical approach to persistent homology. Homology, Ho-motopy Appl. 9 337-362. MR2366953
-
(2007)
Ho-motopy Appl.
, vol.9
, pp. 337-362
-
-
Bubenik, P.1
Kim, P.T.2
-
7
-
-
79751535369
-
Statistical topology via Morse theory persistence and nonparametric estimation
-
Amer. Math. Soc., Providence, RI. MR2730741
-
BUBENIK, P., CARLSSON, G., KIM, P. T. and LUO, Z.-M. (2010). Statistical topology via Morse theory persistence and nonparametric estimation. In Algebraic Methods in Statistics and Probability II. Contemp. Math. 516 75-92. Amer. Math. Soc., Providence, RI. MR2730741
-
(2010)
Algebraic Methods in Statistics and Probability II. Contemp. Math.
, vol.516
, pp. 75-92
-
-
Bubenik, P.1
Carlsson, G.2
Kim, P.T.3
Luo, Z.-M.4
-
9
-
-
67349232288
-
The theory of multidimensional persistence
-
MR2506738
-
CARLSSON, G. and ZOMORODIAN, A. (2009). The theory of multidimensional persistence. Discrete Comput. Geom. 42 71-93. MR2506738
-
(2009)
Discrete Comput. Geom.
, vol.42
, pp. 71-93
-
-
Carlsson, G.1
Zomorodian, A.2
-
11
-
-
57349115995
-
Towards persistence-based reconstruction in Euclidean spaces
-
ACM, New York. MR2504289
-
CHAZAL, F. and OUDOT, S. Y. (2008). Towards persistence-based reconstruction in Euclidean spaces. In Computational Geometry (SCG'08) 232-241. ACM, New York. MR2504289
-
(2008)
Computational Geometry (SCG'08)
, pp. 232-241
-
-
Chazal, F.1
Oudot, S.Y.2
-
13
-
-
79960162399
-
Persistence-based clustering in Riemannian manifolds
-
ACM, New York. MR2919600
-
CHAZAL, F., OUDOT, S., SKRABA, P. and GUIBAS, L. J. (2011). Persistence-based clustering in Riemannian manifolds. In Computational Geometry (SCG'11) 97-106. ACM, New York. MR2919600
-
(2011)
Computational Geometry (SCG'11)
, pp. 97-106
-
-
Chazal, F.1
Oudot, S.2
Skraba, P.3
Guibas, L.J.4
-
14
-
-
84879673260
-
-
Preprint. Available at arXiv: 1207.3674
-
CHAZAL, F., DE SILVA, V., GLISSE, M. and OUDOT, S. (2012). The structure and stability of persistence modules. Preprint. Available at arXiv:1207.3674.
-
(2012)
The Structure and Stability of Persistence Modules
-
-
Chazal, F.1
De Silva, V.2
Glisse, M.3
Oudot, S.4
-
15
-
-
84921529310
-
-
Preprint. Available at arXiv: 1311.0376
-
CHAZAL, F., FASY, B. T., LECCI, F., RINALDO, A., SINGH, A. and WASSERMAN, L. (2013a). On the bootstrap for persistence diagrams and landscapes. Preprint. Available at arXiv:1311.0376.
-
(2013)
On the Bootstrap for Persistence Diagrams and Landscapes
-
-
Chazal, F.1
Fasy, B.T.2
Lecci, F.3
Rinaldo, A.4
Singh, A.5
Wasserman, L.6
-
16
-
-
84904423362
-
-
Preprint. Available at arXiv: 1305.6239
-
CHAZAL, F., GLISSE, M., LABRUÈRE, C. and MICHEL, B. (2013b). Optimal rates of convergence for persistence diagrams in topological data analysis. Preprint. Available at arXiv:1305.6239.
-
(2013)
Optimal Rates of Convergence for Persistence Diagrams in Topological Data Analysis
-
-
Chazal, F.1
Glisse, M.2
Labruère, C.3
Michel, B.4
-
19
-
-
84877925952
-
Set estimation: Another bridge between statistics and geometry
-
MR2750781
-
CUEVAS, A. (2009). Set estimation: Another bridge between statistics and geometry. Bol. Estad. Investig. Oper. 25 71-85. MR2750781
-
(2009)
Bol. Estad. Investig. Oper.
, vol.25
, pp. 71-85
-
-
Cuevas, A.1
-
20
-
-
0035963461
-
Cluster analysis: A further approach based on density estimation
-
MR1855727
-
CUEVAS, A., FEBRERO, M. and FRAIMAN, R. (2001). Cluster analysis: A further approach based on density estimation. Comput. Statist. Data Anal. 36 441-459. MR1855727
-
(2001)
Comput. Statist. Data Anal.
, vol.36
, pp. 441-459
-
-
Cuevas, A.1
Febrero, M.2
Fraiman, R.3
-
21
-
-
0031329212
-
A plug-in approach to support estimation
-
MR1604449
-
CUEVAS, A. and FRAIMAN, R. (1997). A plug-in approach to support estimation. Ann. Statist. 25 2300-2312. MR1604449
-
(1997)
Ann. Statist.
, vol.25
, pp. 2300-2312
-
-
Cuevas, A.1
Fraiman, R.2
-
22
-
-
0032533050
-
On visual distances in density estimation: The Hausdorff choice
-
MR1664548
-
CUEVAS, A. and FRAIMAN, R. (1998). On visual distances in density estimation: The Hausdorff choice. Statist. Probab. Lett. 40 333-341. MR1664548
-
(1998)
Statist. Probab. Lett.
, vol.40
, pp. 333-341
-
-
Cuevas, A.1
Fraiman, R.2
-
23
-
-
84872074050
-
On statistical properties of sets fulfilling rolling-type conditions
-
MR2977397
-
CUEVAS, A., FRAIMAN, R. and PATEIRO-LÓPEZ, B. (2012). On statistical properties of sets fulfilling rolling-type conditions. Adv. in Appl. Probab. 44 311-329. MR2977397
-
(2012)
Adv. in Appl. Probab.
, vol.44
, pp. 311-329
-
-
Cuevas, A.1
Fraiman, R.2
Pateiro-López, B.3
-
25
-
-
0000476095
-
Detection of abnormal behavior via nonparametric estimation of the support
-
MR0579432
-
DEVROYE, L. and WISE, G. L. (1980). Detection of abnormal behavior via nonparametric estimation of the support. SIAM J. Appl. Math. 38 480-488. MR0579432
-
(1980)
SIAM J. Appl. Math.
, vol.38
, pp. 480-488
-
-
Devroye, L.1
Wise, G.L.2
-
26
-
-
70349220130
-
Persistent homology-a survey
-
Amer. Math. Soc, Providence, RI. MR2405684
-
EDELSBRUNNER, H. and HARER, J. (2008). Persistent homology-a survey. In Surveys on Discrete and Computational Geometry. Contemp. Math. 453 257-282. Amer. Math. Soc, Providence, RI. MR2405684
-
(2008)
Surveys on Discrete and Computational Geometry. Contemp. Math.
, vol.453
, pp. 257-282
-
-
Edelsbrunner, H.1
Harer, J.2
-
28
-
-
84908179508
-
-
FASY, B. T., LECCI, F., RINALDO, A., WASSERMAN, L., BALAKRISHNAN, S. and SINGH, A. (2014). Supplement to "Confidence sets for persistence diagrams." DOI:10.1214/14-AOS1252SUPP.
-
(2014)
Supplement to "confidence Sets for Persistence Diagrams."
-
-
Fasy, B.T.1
Lecci, F.2
Rinaldo, A.3
Wasserman, L.4
Balakrishnan, S.5
Singh, A.6
-
29
-
-
84968469617
-
Curvature measures
-
MR0110078
-
FEDERER, H. (1959). Curvature measures. Trans. Amer. Math. Soc. 93 418-491. MR0110078
-
(1959)
Trans. Amer. Math. Soc.
, vol.93
, pp. 418-491
-
-
Federer, H.1
-
30
-
-
41849100389
-
Barcodes: The persistent topology of data
-
MR2358377
-
GHRIST, R. (2008). Barcodes: The persistent topology of data. Bull. Amer. Math. Soc. (N.S.) 45 61-75. MR2358377
-
(2008)
Bull. Amer. Math. Soc. (N.S.)
, vol.45
, pp. 61-75
-
-
Ghrist, R.1
-
31
-
-
0036847557
-
Rates of strong uniform consistency for multivariate kernel density estimators
-
MR1955344
-
GINÉ, E. and GUILLOU, A. (2002). Rates of strong uniform consistency for multivariate kernel density estimators. Ann. Inst. Henri Poincaré Probab. Stat. 38 907-921. MR1955344
-
(2002)
Ann. Inst. Henri Poincaré Probab. Stat.
, vol.38
, pp. 907-921
-
-
Giné, E.1
Guillou, A.2
-
32
-
-
0004193355
-
-
Cambridge Univ. Press, Cambridge. MR1867354
-
HATCHER, A. (2002). Algebraic Topology. Cambridge Univ. Press, Cambridge. MR1867354
-
(2002)
Algebraic Topology
-
-
Hatcher, A.1
-
33
-
-
84864379402
-
Topological analysis of variance and the maxillary complex
-
MR2980059
-
HEO, G., GAMBLE, J. and KIM, P. T. (2012). Topological analysis of variance and the maxillary complex. J. Amer. Statist. Assoc. 107 477-492. MR2980059
-
(2012)
J. Amer. Statist. Assoc.
, vol.107
, pp. 477-492
-
-
Heo, G.1
Gamble, J.2
Kim, P.T.3
-
34
-
-
79960192500
-
Comparing distributions and shapes using the kernel distance
-
ACM, New York. MR2919594
-
JOSHI, S., KOMMARAJU, R. V., PHILLIPS, J. M. and VENKATASUBRAMANIAN, S. (2011). Comparing distributions and shapes using the kernel distance. In Computational Geometry (SCG'11) 47-56. ACM, New York. MR2919594
-
(2011)
Computational Geometry (SCG'11)
, pp. 47-56
-
-
Joshi, S.1
Kommaraju, R.V.2
Phillips, J.M.3
Venkatasubramanian, S.4
-
35
-
-
62149114733
-
Topology of random clique complexes
-
MR2510573
-
KAHLE, M. (2009). Topology of random clique complexes. Discrete Math. 309 1658-1671. MR2510573
-
(2009)
Discrete Math.
, vol.309
, pp. 1658-1671
-
-
Kahle, M.1
-
36
-
-
79751527127
-
Random geometric complexes
-
MR2770552
-
KAHLE, M. (2011). Random geometric complexes. Discrete Comput. Geom. 45 553-573. MR2770552
-
(2011)
Discrete Comput. Geom.
, vol.45
, pp. 553-573
-
-
Kahle, M.1
-
37
-
-
84903767796
-
Limit theorems for Betti numbers of random simplicial complexes
-
MR3079211
-
KAHLE, M. and MECKES, E. (2013). Limit theorems for Betti numbers of random simplicial complexes. Homology, Homotopy Appl. 15 343-374. MR3079211
-
(2013)
Homology, Homotopy Appl.
, vol.15
, pp. 343-374
-
-
Kahle, M.1
Meckes, E.2
-
39
-
-
21844497119
-
Asymptotical minimax recovery of sets with smooth boundaries
-
MR1332579
-
MAMMEN, E. and TSYBAKOV, A. B. (1995). Asymptotical minimax recovery of sets with smooth boundaries. Ann. Statist. 23 502-524. MR1332579
-
(1995)
Ann. Statist.
, vol.23
, pp. 502-524
-
-
Mammen, E.1
Tsybakov, A.B.2
-
41
-
-
82255172087
-
Probability measures on the space of persistence diagrams
-
MR2854323
-
MILEYKO, Y, MUKHERJEE, S. and HARER, J. (2011). Probability measures on the space of persistence diagrams. Inverse Problems 27 124007, 22. MR2854323
-
(2011)
Inverse Problems
, vol.27
-
-
Mileyko, Y.1
Mukherjee, S.2
Harer, J.3
-
42
-
-
0032362040
-
A limit theorem for solutions of inequalities
-
MR1614288
-
MOLCHANOV, I. S. (1998). A limit theorem for solutions of inequalities. Scand. J. Stat. 25 235-242. MR1614288
-
(1998)
Scand. J. Stat.
, vol.25
, pp. 235-242
-
-
Molchanov, I.S.1
-
43
-
-
0032263989
-
Strong approximation of density estimators from weakly dependent observations by density estimators from independent observations
-
MR1673288
-
NEUMANN, M. H. (1998). Strong approximation of density estimators from weakly dependent observations by density estimators from independent observations. Ann. Statist. 26 2014-2048. MR1673288
-
(1998)
Ann. Statist.
, vol.26
, pp. 2014-2048
-
-
Neumann, M.H.1
-
44
-
-
40349102105
-
Finding the homology of submanifolds with high confidence from random samples
-
MR2383768
-
NIYOGI, P., SMALE, S. and WEINBERGER, S. (2008). Finding the homology of submanifolds with high confidence from random samples. Discrete Comput. Geom. 39 419-441. MR2383768
-
(2008)
Discrete Comput. Geom.
, vol.39
, pp. 419-441
-
-
Niyogi, P.1
Smale, S.2
Weinberger, S.3
-
45
-
-
79960379431
-
A topological view of unsupervised learning from noisy data
-
MR2810909
-
NIYOGI, P., SMALE, S. and WEINBERGER, S. (2011). A topological view of unsupervised learning from noisy data. SIAM J. Comput. 40 646-663. MR2810909
-
(2011)
SIAM J. Comput.
, vol.40
, pp. 646-663
-
-
Niyogi, P.1
Smale, S.2
Weinberger, S.3
-
46
-
-
0012535670
-
-
Oxford Studies in Probability 5. Oxford Univ. Press Oxford. MR1986198
-
PENROSE, M. (2003). Random Geometric Graphs. Oxford Studies in Probability 5. Oxford Univ. Press, Oxford. MR1986198
-
(2003)
Random Geometric Graphs
-
-
Penrose, M.1
-
48
-
-
84879136103
-
On the uniform asymptotic validity of subsampling and the bootstrap
-
MR3097960
-
ROMANO, J. P. and SHAIKH, A. M. (2012). On the uniform asymptotic validity of subsampling and the bootstrap. Ann. Statist. 40 2798-2822. MR3097960
-
(2012)
Ann. Statist.
, vol.40
, pp. 2798-2822
-
-
Romano, J.P.1
Shaikh, A.M.2
-
49
-
-
84904427571
-
Fréchet Means for Distributions of Persistence Diagrams
-
MR3231030
-
TURNER, K., MILEYKO, Y., MUKHERJEE, S. and HARER, J. (2014). Fréchet Means for Distributions of Persistence Diagrams. Discrete Comput. Geom. 52 44-70. MR3231030
-
(2014)
Discrete Comput. Geom.
, vol.52
, pp. 44-70
-
-
Turner, K.1
Mileyko, Y.2
Mukherjee, S.3
Harer, J.4
|