This is a collection of papers by participants at the High Dimensional Probability VI Meeting held from October 9-14, 2011 at the Banff International Research Station in Banff, Alberta, Canada. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range of application has led to interactions with other areas of mathematics, statistics, and computer science. These include random matrix theory, nonparametric statistics, empirical process theory, statistical learning theory, concentration of measure phenomena, strong and weak approximations, distribution function estimation in high dimensions, combinatorial optimization, and random graph theory. The papers in this volume show that HDP theory continues to develop new tools, methods, techniques and perspectives to analyze the random phenomena. Both researchers and advanced students will find this book of great use for learning about new avenues of research.​

lgrsnf/M_Mathematics/MV_Probability/Houdre C., et al. (eds.) High dimensional probability VI. The Banff volume (Birkhauser, 2013)(ISBN 9783034804899)(O)(367s)_MV_.pdf

nexusstc/High Dimensional Probability VI: The Banff Volume/58084f3ad2da1a9b10839215c71339ec.pdf

scihub/10.1007/978-3-0348-0490-5.pdf

zlib/Computers/Computer Science/Houdre, Christian; Mason, David M.; Rosinski, Jan; Wellner, Jon A (eds.)/High Dimensional Probability VI The Banff Volume_2079173.pdf

High Dimensional Probability VI [recurso electrónico] The Banff Volume

Christian Houdré; David M Mason; Jan Rosiński; Jon A Wellner; International Conference on High Dimensional Probability

edited by Christian Houdré, David M. Mason, Jan Rosiński, Jon A. Wellner

Springer Nature Switzerland AG

Birkhauser

Birkh User

Progress in probability, v. 66, Basel [Switzerland, 2013

Progress in probability, Hoboken, N.J, 2013

Progress in probability, Basel [etc, 2013

Progress in Probability, uuuu

Springer Nature, Basel, 2013

Switzerland, Switzerland

2012

Kolxo3 -- 63-64

lg925068

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MiU

Cover......Page 1
Contents......Page 6
Preface......Page 8
Inequalities and Convexity:......Page 9
Limit Theorems:......Page 10
Random Matrices and Applications:......Page 11
High Dimensional Statistics:......Page 12
Participants......Page 13
Dedication......Page 14
1. Introduction......Page 15
2. Bracketing entropy estimate......Page 19
3. Bounding bracketing entropy using metric entropy......Page 26
References......Page 28
1. Introduction......Page 30
2. Slepian’s inequality......Page 33
3. Integral orderings......Page 46
4. Modular orderings......Page 52
References......Page 63
1. Introduction......Page 65
Acknowledgment......Page 71
References......Page 72
1. Introduction and main results......Page 73
2. Proofs......Page 76
3. Example......Page 80
References......Page 81
1. Introduction......Page 82
2. Main result......Page 83
3. A relation to random processes......Page 86
4. Relation to bifractional Brownian motion......Page 87
References......Page 88
1. Introduction......Page 90
2. Summary and discussion......Page 91
3. Application: Rosenthal-type concentration inequalities for separately Lipschitz functions on product spaces......Page 94
4. Proofs......Page 96
References......Page 101
1. Log-concavity and ultra-log-concavity for discrete distributions......Page 103
2. Log-concavity and strong-log-concavity for continuous distributions on R......Page 106
References......Page 109
1. Introduction......Page 111
2. The result......Page 112
3. Application to U-statistics......Page 117
References......Page 118
1. Introduction and notations......Page 119
2. ASIP with rates for ergodic automorphisms of the torus......Page 121
3. Probabilistic results......Page 123
4.1. Preparatory material......Page 135
5. Appendix......Page 141
References......Page 143
1. Introduction......Page 145
2. Bounds for the Kolmogorov distance between distribution functions via Stieltjes transforms......Page 147
3. Large deviations I......Page 152
4. Bounds for ∣mn(z)∣......Page 157
5. Large deviations II......Page 159
6. Stieltjes transforms......Page 164
7. Proof of Theorem 1.1......Page 167
8. Proof of Theorem 1.2......Page 169
References......Page 170
1. Introduction......Page 172
2. Statement of results......Page 175
3.1. Notation and some lemmas......Page 178
3.2. Applying Lemma 2 to obtain an empirical quantile CLT......Page 182
3.3. Proof of Theorem 1......Page 187
4. Proof of Theorem 2......Page 189
4.1. Gaussian process empirical CLT’s over C......Page 190
4.2. Compound Poisson process empirical CLT’s over C......Page 193
4.3. Empirical process CLT’s over C for other independent increment processes and martingales ......Page 194
References......Page 199
1. Introduction......Page 200
2. Definitions, background and results......Page 202
3.1. Application to a Metropolis Hastings Markov chain......Page 206
3.3. Application to random walks on compact groups......Page 207
4.1. Preliminary general results......Page 208
4.2. Normal and reversible Markov chains......Page 210
5. Appendix......Page 213
References......Page 214
1. Introduction......Page 216
2. Proof......Page 217
3. Further remarks......Page 219
References......Page 220
1. Introduction......Page 221
2. Lévy’s Equivalence Theorem for D([0, 1];E)......Page 223
References......Page 227
1. Introduction......Page 228
2. Continuity......Page 233
3. Proof of Theorem 1.1......Page 234
4. Domination by the second moment......Page 242
References......Page 244
1. Introduction......Page 245
2. Proof of Theorem 1.1......Page 248
3. Proof of Proposition 1.2......Page 254
4. Appendix......Page 255
References......Page 257
1. Introduction......Page 259
2. Global moderate deviations at the edge of the spectrum......Page 261
3. Local moderate deviations at the edge of the spectrum......Page 263
4. Universal local moderate deviations near the edge......Page 266
5. Universal global moderate deviations near the edge......Page 268
6. Further random matrix ensembles......Page 271
References......Page 272
1. Introduction......Page 274
2. Generalized traceless GUE......Page 276
3. Young diagrams and inhomogeneous random words......Page 279
4. The Poissonized Word Problem......Page 287
5. Appendix......Page 293
References......Page 297
1. Introduction......Page 300
2. Main results......Page 304
3. Proofs......Page 307
References......Page 319
1. Introduction......Page 321
2. Tools and definitions......Page 325
3. Main results for sparse PCA with missing observations......Page 326
4.1. Proof of Propositions 2 and 3......Page 332
4.2. Proof of Theorems 1 and 2......Page 335
4.3. Proof of Lemma 2......Page 337
4.4. Proof of Theorem 4......Page 338
4.6. Proof of Lemma 5......Page 340
4.7. Proof of Fact 1......Page 341
4.8. Proof of Fact 2......Page 342
4.9. Bounding of the moment E[(θT Zθ)2] ......Page 347
References......Page 349
1. Introduction......Page 351
2. Main results......Page 353
Quantile approximation justification......Page 356
Application......Page 357
GOF test......Page 358
Comments for Table 3.1......Page 359
4. Proofs......Page 360
References......Page 367

Provides an introduction to what is meant by high dimensional probability and exposes new areas of research in the area. Covers mathematical methods used by experts to establish limit theorems in probability and statistics which reside in high dimensions

2013-05-29