Statistics 607b, Spring 2005: References

  1. Tails of the normal distribution: classical bounds; Mill's ratio; conditional distributions; LIL.

  2. Convexity: log moment generating functions; Hoeffding's inequality; Bennett's inequality; large deviation bounds; Orlicz norms; subgaussian distributions.

  3. Metric entropy: chaining inequality for processes via Orlicz norms; Gaussian processes.

  4. Distances between measures: total variation; Hellinger; Kullback-Leibler; Fano's lemma; Assouad's inequality; minimax rates of convergence; maximum likelihood in one dimension via Hellinger distance.

  5. Covariance inequalities: FKG; application to 2-dimensional Ising model.

  6. Combinatorial bounds: Vapnik-Cervonenkis and beyond.

  7. Concentration inequalities: martingale method; Talagrand's method for product measures; tensorization methods.

  8. Poisson and Binomial: coupling bound; Le Cam-Hodges method; Chen-Stein method; unimodality; majorization.

  9. Berry-Esseen bound: via Fourier inversion method; Stein's method.

  10. Tusnady's inequality: coupling of empirical and Gaussian processes.

  11. Majorizing measures: the "generic chaining".

  12. Sudakov and Fernique inequalities for Gaussian processes; Borell's isopermetric inequality.

Bibtex citations

Most references are given in the form of a Bibtex record. Talk with DP if you do not know how to compile lists of references using Bibtex. I have included a URL field in some cases, even though the version of Bibtex on my computer does not handle it correctly. If you create your own bib file, you would need to put commands like 
@STRING{annprob="Annals of Probability"}
@string{cup="Cambridge University Press"}
at the start of the file if you want to refer to journals by abbreviations.

For my own work I have created DBP.bib. 

@article{CarterPollard00tusnady,
author = {Andrew Carter and David Pollard},
title = {Tusn\'ady's inequality revisited},
journal = annstat,
year = 2004,
volume="32",
pages="???--???"
}

@article{Csiszar75AP,
TITLE = "I-Divergence Geometry of Probability Distributions and Minimization Problems",
AUTHOR = "I. Csiszar",
JOURNAL="The Annals of Probability",
VOLUME = "3",
NUMBER = "1",
MONTH = "Feb",
YEAR = "1975",
PAGES = "146-158",
URL = "http://links.jstor.org/sici?sici=0091-1798%28197502%293%3A1%3C146%3AGOPDAM%3E2.0.CO%3B2-R",
}

@book{Feller1,
 author = "William Feller",
 title = "An Introduction to Probability Theory and Its Applications",
 publisher = "Wiley",
 year = "1968",
 volume = "1",
 address = "New York",
 edition = "third",
}

@book{LeadbetterLindgrenRootzen83,
 author = "M. R. Leadbetter and Georg Lindgren and Holger Rootz{\'e}n",
 title = "Extremes and Related Properties of Random Sequences and Processes",
 publisher = springer,
 year = "1983",
}


@book{Ledoux01conc,
 author = {Michel Ledoux},
 title = {The Concentration of Measure Phenomenon},
 publisher = {American Mathematical Society},
 year = {2001}, 
 series = {Mathematical Surveys and Monographs}, 
 volume = {89},
}

@book{PollardUGMTP,
 author = "David Pollard",
 title = "A User's Guide to Measure Theoretic Probability",
 publisher = cup,
 year = 2001,
 note = "Some samples at http://www.stat.yale.edu/\~\/pollard"
}

@article{Talagrand95IHES,
AUTHOR = {Michel Talagrand},
TITLE = {Concentration of measure and isoperimetric inequalities 
in product spaces},
JOURNAL = {Publications Math\'ematiques de l'{I.H.E.S.}},
YEAR = {1995},
VOLUME = {81},
PAGES = {73--205} }

@article{Talagrand96IM,
AUTHOR = {Michel Talagrand},
TITLE = {New concentration inequalities in product spaces},
JOURNAL = {Inventiones mathematicae},
YEAR = {1996},
VOLUME = {126},
PAGES = {505--563} }

@article{Talagrand96newlook,
AUTHOR = {Michel Talagrand},
TITLE = {A new look at independence},
JOURNAL = annprob,
YEAR = {1996},
VOLUME = {24},
PAGES = {1--34} }

@article{Talagrand96MM,
AUTHOR = {Michel Talagrand},
TITLE = {Majorizing Measures: The Generic Chaining (in Special Invited Paper)},
JOURNAL = annprob,
YEAR = {1996},
VOLUME = {24},
PAGES = {1049-1103},
URL={http://links.jstor.org/sici?sici=0091-1798%28199607%2924%3A3%3C1049%3AMMTGC%3E2.0.CO%3B2-T},
}