High Dimensional Probability VI

Name: High Dimensional Probability VI | The Banff Volume
Brand: Birkhäuser
Price: 149.79 EUR
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The Banff Volume

Christian Houdré David M. Mason Jan Rosinski Jon A. Wellner(Herausgeber*in)

Birkhäuser (Verlag)

Erschienen am 19. April 2013

XIII, 374 Seiten

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978-3-0348-0490-5 (ISBN)

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Inhalt

Intro
Contents
Preface
Inequalities and Convexity:
Limit Theorems:
Stochastic Processes:
Random Matrices and Applications:
High Dimensional Statistics:
Participants
Dedication
Part I Inequalities and Convexity
Bracketing Entropy of High Dimensional Distributions
1. Introduction
2. Bracketing entropy estimate
3. Bounding bracketing entropy using metric entropy
Acknowledgement
References
Slepian's Inequality, Modularity and Integral Orderings
1. Introduction
2. Slepian's inequality
3. Integral orderings
4. Modular orderings
References
A More General Maximal Bernstein-type Inequality
1. Introduction
Acknowledgment
References
Maximal Inequalities for Centered Norms of Sums of Independent Random Vectors
1. Introduction and main results
2. Proofs
3. Example
References
A Probabilistic Inequality Related to Negative Definite Functions
1. Introduction
2. Main result
3. A relation to random processes
4. Relation to bifractional Brownian motion
5. A counterexample
Acknowledgement
References
Optimal Re-centering Bounds, with Applications to Rosenthal-type Concentration of Measure Inequalities
1. Introduction
2. Summary and discussion
3. Application: Rosenthal-type concentration inequalities for separately Lipschitz functions on product spaces
4. Proofs
Acknowledgment
References
Strong Log-concavity is Preserved by Convolution
1. Log-concavity and ultra-log-concavity for discrete distributions
2. Log-concavity and strong-log-concavity for continuous distributions on R
3. Appendix: strong convexity and strong log-concavity
Acknowledgment
References
On Some Gaussian Concentration Inequality for Non-Lipschitz Functions
1. Introduction
2. The result
3. Application to U-statistics
References
Part II Limit Theorems
Rates of Convergence in the Strong Invariance Principle for Non-adapted Sequences. Application to Ergodic Automorphisms of the Torus
1. Introduction and notations
2. ASIP with rates for ergodic automorphisms of the torus
3. Probabilistic results
4. Proof of Theorem 2.1
4.1. Preparatory material
4.2. End of the proof of Theorem 2.1
5. Appendix
References
On the Rate of Convergence to the Semi-circular Law
1. Introduction
2. Bounds for the Kolmogorov distance between distribution functions via Stieltjes transforms
3. Large deviations I
4. Bounds for │mn(z)│
5. Large deviations II
6. Stieltjes transforms
7. Proof of Theorem 1.1
8. Proof of Theorem 1.2
Acknowledgement
References
Empirical Quantile CLTs for Time-dependent Data
1. Introduction
2. Statement of results
3. The proof of Theorem 1: Vervaat's approach
3.1. Notation and some lemmas
3.2. Applying Lemma 2 to obtain an empirical quantile CLT
3.3. Proof of Theorem 1
4. Proof of Theorem 2
4.1. Gaussian process empirical CLT's over C
4.2. Compound Poisson process empirical CLT's over C
4.3. Empirical process CLT's over C for other independent increment processes and martingales
References
Asymptotic Properties for Linear Processes of Functionals of Reversible or Normal Markov Chains
1. Introduction
2. Definitions, background and results
3. Applications
3.1. Application to a Metropolis Hastings Markov chain
3.2. Linear process of instantaneous functions of a Gaussian sequence
3.3. Application to random walks on compact groups
4. Proofs
4.1. Preliminary general results
4.2. Normal and reversible Markov chains
5. Appendix
Acknowledgement
References
Part III Stochastic Processes
First Exit of Brownian Motion from a One-sided Moving Boundary
1. Introduction
2. Proof
3. Further remarks
References
On Lévy's Equivalence Theorem in Skorohod Space
1. Introduction
1.1. Definitions and notations
2. Lévy's Equivalence Theorem for D([0, 1]
E)
References
Continuity Conditions for a Class of Second-order Permanental Chaoses
1. Introduction
2. Continuity
3. Proof of Theorem 1.1
4. Domination by the second moment
References
Part IV Random Matrices and Applications
On the Operator Norm of Random Rectangular Toeplitz Matrices
1. Introduction
2. Proof of Theorem 1.1
3. Proof of Proposition 1.2
4. Appendix
References
Edge Fluctuations of Eigenvalues of Wigner Matrices
1. Introduction
2. Global moderate deviations at the edge of the spectrum
3. Local moderate deviations at the edge of the spectrum
4. Universal local moderate deviations near the edge
5. Universal global moderate deviations near the edge
6. Further random matrix ensembles
Acknowlegement
References
On the Limiting Shape of Young Diagrams Associated with Inhomogeneous Random Words
1. Introduction
2. Generalized traceless GUE
3. Young diagrams and inhomogeneous random words
4. The Poissonized Word Problem
5. Appendix
Acknowledgment
References
Part V High Dimensional Statistics
Low Rank Estimation of Similarities on Graphs
1. Introduction
2. Main results
3. Proofs
References
Sparse Principal Component Analysis with Missing Observations
1. Introduction
2. Tools and definitions
3. Main results for sparse PCA with missing observations
4. Proofs
4.1. Proof of Propositions 2 and 3
4.2. Proof of Theorems 1 and 2
4.3. Proof of Lemma 2
4.4. Proof of Theorem 4
4.5. Proof of Lemma 4
4.6. Proof of Lemma 5
4.7. Proof of Fact 1
4.8. Proof of Fact 2
4.9. Bounding of the moment E[(?T Z?)2]
References
High Dimensional CLT and its Applications
1. Introduction
2. Main results
3. Applications
Quantile approximation justification
Application
GOF test
Numerical results
Comments for Table 3.1
4. Proofs
References

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