Ebook: High Dimensional Probability III
Author: J. Hoffmann-Jørgensen (auth.) Jørgen Hoffmann-Jørgensen Jon A. Wellner Michael B. Marcus (eds.)
- Tags: Measure and Integration, Probability Theory and Stochastic Processes, Statistics general
- Series: Progress in Probability 55
- Year: 2003
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
The title High Dimensional Probability is an attempt to describe the many trib utaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970's. In each of these fields it is necessary to consider large classes of stochastic processes under minimal conditions. There are rewards in re search of this sort. One can often gain deep insights, even about familiar processes, by stripping away details that in hindsight turn out to be extraneous. Many of the problems that motivated researchers in the 1970's were solved. But the powerful new tools created for their solution, such as randomization, isoperimetry, concentration of measure, moment and exponential inequalities, chaining, series representations and decoupling turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new ap proach to the study of aspects of Levy processes and Markov processes in general. Papers on these topics as well as on the continuing study of Gaussian processes and probability in Banach are included in this volume.
Content:
Front Matter....Pages i-viii
Front Matter....Pages 1-1
Stochastic inequalities and perfect independence....Pages 3-34
Prokhorov—LeCam—Varadarajan’s Compactness Criteria for Vector Measures on Metric Spaces....Pages 35-42
On Measures in Locally Convex Spaces....Pages 43-54
Front Matter....Pages 55-55
Karhunen-Lo?ve Expansions for Weighted Wiener Processes and Brownian Bridges via Bessel Functions....Pages 57-93
Extension du th?or?me de Cameron-Martin aux translations al?atoires. II. Int?grabilit? des densit?s....Pages 95-102
Front Matter....Pages 103-103
Rates of Convergence for L?vy’s Modulus of Continuity and Hinchin’s Law of the Iterated Logarithm....Pages 105-109
On the Limit Set in the Law of the Iterated Logarithm for U-statistics of Order Two....Pages 111-126
Perturbation Approach Applied to the Asymptotic Study of Random Operators....Pages 127-134
A Uniform Functional Law of the Logarithm for a Local Gaussian Process....Pages 135-151
Strong Limit Theorems for Mixing Random Variables with Values in Hilbert Space and their Applications....Pages 153-174
Front Matter....Pages 175-175
Local Time-Space Calculus and Extensions of It?’s Formula....Pages 177-192
Local Times on Curves and Surfaces....Pages 193-202
Front Matter....Pages 203-203
Large Deviations of Empirical Processes....Pages 205-223
Small Deviation Estimates for Some Additive Processes....Pages 225-238
Front Matter....Pages 239-239
Convergence in Distribution of Self-Normalized Sup-Norms of Kernel Density Estimators....Pages 241-253
Estimates of the Rate of Approximation in the CLT for L 1-Norm of Density Estimators....Pages 255-292
Front Matter....Pages 293-293
Statistical Nearly Universal Glivenko—Cantelli Classes....Pages 295-312
Smoothed Empirical Processes and the Bootstrap....Pages 313-320
A Note on the Asymptotic Distribution of Berk—Jones Type Statistics under the Null Hypothesis....Pages 321-332
A Note on the Smoothed Bootstrap....Pages 333-346
Content:
Front Matter....Pages i-viii
Front Matter....Pages 1-1
Stochastic inequalities and perfect independence....Pages 3-34
Prokhorov—LeCam—Varadarajan’s Compactness Criteria for Vector Measures on Metric Spaces....Pages 35-42
On Measures in Locally Convex Spaces....Pages 43-54
Front Matter....Pages 55-55
Karhunen-Lo?ve Expansions for Weighted Wiener Processes and Brownian Bridges via Bessel Functions....Pages 57-93
Extension du th?or?me de Cameron-Martin aux translations al?atoires. II. Int?grabilit? des densit?s....Pages 95-102
Front Matter....Pages 103-103
Rates of Convergence for L?vy’s Modulus of Continuity and Hinchin’s Law of the Iterated Logarithm....Pages 105-109
On the Limit Set in the Law of the Iterated Logarithm for U-statistics of Order Two....Pages 111-126
Perturbation Approach Applied to the Asymptotic Study of Random Operators....Pages 127-134
A Uniform Functional Law of the Logarithm for a Local Gaussian Process....Pages 135-151
Strong Limit Theorems for Mixing Random Variables with Values in Hilbert Space and their Applications....Pages 153-174
Front Matter....Pages 175-175
Local Time-Space Calculus and Extensions of It?’s Formula....Pages 177-192
Local Times on Curves and Surfaces....Pages 193-202
Front Matter....Pages 203-203
Large Deviations of Empirical Processes....Pages 205-223
Small Deviation Estimates for Some Additive Processes....Pages 225-238
Front Matter....Pages 239-239
Convergence in Distribution of Self-Normalized Sup-Norms of Kernel Density Estimators....Pages 241-253
Estimates of the Rate of Approximation in the CLT for L 1-Norm of Density Estimators....Pages 255-292
Front Matter....Pages 293-293
Statistical Nearly Universal Glivenko—Cantelli Classes....Pages 295-312
Smoothed Empirical Processes and the Bootstrap....Pages 313-320
A Note on the Asymptotic Distribution of Berk—Jones Type Statistics under the Null Hypothesis....Pages 321-332
A Note on the Smoothed Bootstrap....Pages 333-346
....