@article{Bar_Bir_Mas:1999,
    AUTHOR = {Barron, Andrew and Birg{\'e}, Lucien and Massart, Pascal},
     TITLE = {Risk bounds for model selection via penalization},
   JOURNAL = {Probab. Theory Related Fields},
  FJOURNAL = {Probability Theory and Related Fields},
    VOLUME = {113},
      YEAR = {1999},
    NUMBER = {3},
     PAGES = {301--413},
      ISSN = {0178-8051},
     CODEN = {PTRFEU},
   MRCLASS = {62G05 (62G07 65C60)},
  MRNUMBER = {MR1679028 (2000k:62049)},
MRREVIEWER = {Friedrich Liese},
}

@article {Bir_Mas:1998,
    AUTHOR = {Birg{\'e}, Lucien and Massart, Pascal},
     TITLE = {Minimum contrast estimators on sieves: exponential bounds and
              rates of convergence},
   JOURNAL = {Bernoulli},
  FJOURNAL = {Bernoulli. Official Journal of the Bernoulli Society for
              Mathematical Statistics and Probability},
    VOLUME = {4},
      YEAR = {1998},
    NUMBER = {3},
     PAGES = {329--375},
      ISSN = {1350-7265},
   MRCLASS = {62G07 (62G08 62G20)},
  MRNUMBER = {MR1653272 (2000g:62071)},
MRREVIEWER = {Yves Lepage},
}

@book {Vap_Cer:1974,
    AUTHOR = {Vapnik, Vladimir N. and Chervonenkis, Alexey Ya.},
     TITLE = {Teoriya raspoznavaniya obrazov. {S}tatisticheskie problemy
              obucheniya},
      NOTE = {Theory of Pattern Recognition (In Russian)},
 PUBLISHER = {Izdat. ``Nauka''},
   ADDRESS = {Moscow},
     YEAR = {1974},
     PAGES = {415},
   MRCLASS = {62H30 (68A45)},
  MRNUMBER = {MR0474638 (57 \#14274)},
MRREVIEWER = {R. M. Dudley},
}

@book {Vap:1998,
    AUTHOR = {Vapnik, Vladimir N.},
     TITLE = {Statistical learning theory},
 PUBLISHER = {John Wiley \& Sons Inc.},
   ADDRESS = {New York},
      YEAR = {1998},
     PAGES = {xxvi+736},
      ISBN = {0-471-03003-1},
   MRCLASS = {62G07 (68T05)},
  MRNUMBER = {99h:62052},
MRREVIEWER = {Ilya S. Molchanov},
} 

@incollection {Lug:2002,
    AUTHOR = {Lugosi, G{\'a}bor},
     TITLE = {Pattern classification and learning theory},
 BOOKTITLE = {Principles of nonparametric learning (Udine, 2001)},
    SERIES = {CISM Courses and Lectures},
    VOLUME = {434},
     PAGES = {1--56},
 PUBLISHER = {Springer},
   ADDRESS = {Vienna},
      YEAR = {2002},
   MRCLASS = {68T10 (62H30 68Q32 68T05 91E40)},
  MRNUMBER = {2004e:68090},
MRREVIEWER = {Witold Pedrycz},
}

@article{Dev_Lug:1995,
    AUTHOR = {Devroye, Luc and Lugosi, G{\'a}bor},
    TITLE = {Lower bounds in pattern recognition and learning},
   JOURNAL = {Pattern Recognition},
  FJOURNAL = {Pattern Recognition},
    VOLUME = {28},
      YEAR = {1995},
    NUMBER = {7},
     PAGES = {1011--1018},
    }   

@article {Kol:2006,
    AUTHOR = {Koltchinskii, Vladimir},
     TITLE = {Local {R}ademacher complexities and oracle inequalities in
              risk minimization},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {34},
      YEAR = {2006},
    NUMBER = {6},
     PAGES = {2593--2656},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62G30 (62H30 68T05)},
  MRNUMBER = {MR2329442},
}
    
@article{Bla_Mas:2006,
    AUTHOR = {Blanchard, Gilles and Massart, Pascal},
     TITLE = {Discussion: ``{L}ocal {R}ademacher complexities and oracle
              inequalities in risk minimization'' [{A}nn. {S}tatist. {\bf
              34} (2006), no. 6, 2593--2656] by {V}.
              {K}oltchinskii},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {34},
      YEAR = {2006},
    NUMBER = {6},
     PAGES = {2664--2671},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62G30 (62H30)},
  MRNUMBER = {MR2329460},
}

@article{vdG:2006,
    AUTHOR = {van de Geer, Sara},
     TITLE = {Discussion: ``{L}ocal {R}ademacher complexities and oracle
              inequalities in risk minimization'' [{A}nn. {S}tatist. {\bf
              34} (2006), no. 6, 2593--2656] by {V}.
              {K}oltchinskii},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {34},
      YEAR = {2006},
    NUMBER = {6},
     PAGES = {2688--2696},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62G30 (62H30 68T05)},
  MRNUMBER = {MR2329463},
}

@article{Bar_Men:2006b,
    AUTHOR = {Bartlett, Peter L. and Mendelson, Shahar},
     TITLE = {Discussion: ``{L}ocal {R}ademacher complexities and oracle
              inequalities in risk minimization'' [{A}nn. {S}tatist. {\bf
              34} (2006), no. 6, 2593--2656] by {V}.
              {K}oltchinskii},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {34},
      YEAR = {2006},
    NUMBER = {6},
     PAGES = {2657--2663},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62G30},
  MRNUMBER = {MR2329459},
}

@article {Cle_Lug_Vay:2006,
    AUTHOR = {Cl{\'e}men{\c{c}}on, St{\'e}phan and Lugosi, G{\'a}bor and
              Vayatis, Nicolas},
     TITLE = {Discussion: ``{L}ocal {R}ademacher complexities and oracle
              inequalities in risk minimization'' [{A}nn. {S}tatist. {\bf
              34} (2006), no. 6, 2593--2656] by {V}.
              {K}oltchinskii},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {34},
      YEAR = {2006},
    NUMBER = {6},
     PAGES = {2672--2676},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62G30 (62H30 68T05)},
  MRNUMBER = {MR2329467},
}

@article {Tsy:2006,
    AUTHOR = {Tsybakov, A. B.},
     TITLE = {Discussion: ``{L}ocal {R}ademacher complexities and oracle
              inequalities in risk minimization'' [{A}nn. {S}tatist. {\bf
              34} (2006), no. 6, 2593--2656] by {V}.
              {K}oltchinskii},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {34},
      YEAR = {2006},
    NUMBER = {6},
     PAGES = {2681--2687},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62G30 (62H30 68T05)},
  MRNUMBER = {MR2329462},
}

@article {She_Wan:2006,
    AUTHOR = {Shen, Xiaotong and Wang, Lifeng},
     TITLE = {Discussion: ``{L}ocal {R}ademacher complexities and oracle
              inequalities in risk minimization'' [{A}nn. {S}tatist. {\bf
              34} (2006), no. 6, 2593--2656] by {V}.
              {K}oltchinskii},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {34},
      YEAR = {2006},
    NUMBER = {6},
     PAGES = {2677--2680},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62G30 (62H30 68T05)},
  MRNUMBER = {MR2329461},
}
    
@ARTICLE{Bar:2007,
  AUTHOR = {Peter L. Bartlett},
  TITLE = {Fast rates for estimation error and oracle
	inequalities for model selection},
  YEAR = {2008},
  JOURNAL = {Econometric Theory},
  VOLUME = {24},
  NUMBER = {2},
  PDF = {http://www.stat.berkeley.edu/~bartlett/papers/b-freeoims-07.pdf},
  NOTE = {(To appear. Was Department of Statistics,
U.C.\ Berkeley Technical Report number 729, 2007)},
}

@ARTICLE{Bar_Men:2006,
  AUTHOR = {Peter L.~Bartlett and Shahar Mendelson},
  TITLE = {Empirical minimization},
  JOURNAL = {Probability Theory and Related Fields},
  YEAR = {2006},
  VOLUME = 135,
  NUMBER = 3,
  PAGES = {311--334},
  PS = {http://www.stat.berkeley.edu/~bartlett/papers/bm-em-05.ps.gz},
  PDF = {http://www.stat.berkeley.edu/~bartlett/papers/bm-em-05.pdf},
  }
  
@ARTICLE{Bar_Bou_Men:2005,
  TITLE = {Local {R}ademacher complexities},
  AUTHOR = {Peter L.~Bartlett and Olivier Bousquet and Shahar Mendelson},
  PS = {http://www.stat.berkeley.edu/~bartlett/papers/bbm-lrc-05.ps},
  PDF = {http://www.stat.berkeley.edu/~bartlett/papers/bbm-lrc-05.pdf},
  JOURNAL = {Annals of Statistics},
  VOLUME = {33},
  NUMBER = {4},
  PAGES = {1497--1537},
  YEAR = {2005},
}
  
@ARTICLE{Bar_Jor_McA:2006,
  TITLE = {Convexity, classification, and risk bounds},
  AUTHOR = {Peter L.\ Bartlett and
  Michael I.\ Jordan and Jon D.\ McAuliffe},
  YEAR = {2006},
  JOURNAL = {Journal of the American Statistical Association},
  VOLUME = {101},
  NUMBER = {473},
  PAGES = {138-156},
  PS = {http://www.stat.berkeley.edu/~bartlett/papers/bjm-ccrb-05.ps.gz},
  PDF = {http://www.stat.berkeley.edu/~bartlett/papers/bjm-ccrb-05.pdf},
}

@article {Tsy:2004,
    AUTHOR = {Tsybakov, Alexandre B.},
     TITLE = {Optimal aggregation of classifiers in statistical learning},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {32},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {135--166},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62H30 (62G08 68T10)},
  MRNUMBER = {2 051 002},
}

@article {Mam_Tsy:1999,
    AUTHOR = {Mammen, Enno and Tsybakov, Alexandre B.},
     TITLE = {Smooth discrimination analysis},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {27},
      YEAR = {1999},
    NUMBER = {6},
     PAGES = {1808--1829},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62H30 (62G05 62G20)},
  MRNUMBER = {MR1765618 (2001i:62074)},
}

@article{Mas_Ned:2003,
    AUTHOR = {Massart, Pascal and N{\'e}d{\'e}lec, {\'E}lodie},
     TITLE = {Risk bounds for statistical learning},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {34},
      YEAR = {2006},
    NUMBER = {5},
     PAGES = {2326--2366},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62H30 (60E15 60F10 68Q32)},
  MRNUMBER = {MR2291502},
}

@incollection {Bar_Men_Phi:2004,
    AUTHOR = {Bartlett, Peter L. and Mendelson, Shahar and Philips, Petra},
     TITLE = {Local complexities for empirical risk minimization},
 BOOKTITLE = {Learning theory},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {3120},
     PAGES = {270--284},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2004},
   MRCLASS = {62G05 (68T05)},
  MRNUMBER = {MR2177915 (2006h:62033)},
MRREVIEWER = {Winfried Stute},
}

@article {Lug_Weg:2004,
    AUTHOR = {Lugosi, G{\'a}bor and Wegkamp, Marten},
     TITLE = {Complexity regularization via localized random penalties},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {32},
      YEAR = {2004},
    NUMBER = {4},
     PAGES = {1679--1697},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62H30 (62C99)},
  MRNUMBER = {MR2089138 (2005h:62169)},
MRREVIEWER = {Tapan K. Nayak},
}

%%% By aggregation


@phdthesis{ Lec:2007a,
    AUTHOR = {Lecu{\'e}, Guillaume},
     TITLE = {M{\'e}thodes d'Agr{\'e}gation : Optimalit{\'e} et Vitesses Rapides},
      YEAR = {2007},
     MONTH = may,
    SCHOOL = {LPMA, University Paris VII},
}

@article {Lec:2007c,
    AUTHOR = {Lecu{\'e}, Guillaume},
     TITLE = {Simultaneous adaptation to the margin and to complexity in
              classification},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {35},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {1698--1721},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62G05 (62H30)},
  MRNUMBER = {MR2351102},
}

@incollection {Lec:2007b,
    AUTHOR = {Lecu{\'e}, Guillaume},
     TITLE = {Suboptimality of Penalized Empirical Risk Minimization in Classification},
 BOOKTITLE = {COLT 2007},
    SERIES = {Lecture Notes in Artificial Intelligence},
    VOLUME = {4539},
     PAGES = {},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2007},
}

%%% Margin without local Rademacher complexities

@article {Tsy_vdG:2005,
    AUTHOR = {Tsybakov, Alexandre B. and van de Geer, Sara A.},
     TITLE = {Square root penalty: adaptation to the margin in
              classification and in edge estimation},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {33},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {1203--1224},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62H30 (62G07 62G08 68T10)},
  MRNUMBER = {MR2195633 (2007d:62032)},
MRREVIEWER = {P. Laurie Davies},
}
  
@unpublished{Aud:2004:PMA908,
    AUTHOR = {Audibert, Jean-Yves},
     TITLE = {Classification under polynomial entropy and margin assumptions and randomized estimators},
      YEAR = {2004},
      NOTE = {Preprint, Laboratoire de Probabilites et Modeles Aleatoires},
       PDF = {http://www.proba.jussieu.fr/mathdoc/textes/PMA-908.pdf},
  }
  
%%%% Using convex risk minimization (or plug-in rules)

@article {Bla_Lug_Vay:2003,
    AUTHOR = {Blanchard, Gilles and Lugosi, G{\'a}bor and Vayatis, Nicolas},
     TITLE = {On the rate of convergence of regularized boosting
              classifiers},
   JOURNAL = {J. Mach. Learn. Res.},
  FJOURNAL = {Journal of Machine Learning Research (JMLR)},
    VOLUME = {4},
      YEAR = {2004},
    NUMBER = {5},
     PAGES = {861--894},
      ISSN = {1532-4435},
   MRCLASS = {62H30 (68Q32 68T05)},
  MRNUMBER = {MR2076000 (2005k:62156)},
MRREVIEWER = {Witold Pedrycz},
}


@article {Aud_Tsy:2007,
    AUTHOR = {Audibert, Jean-Yves and Tsybakov, Alexandre B.},
     TITLE = {Fast learning rates for plug-in classifiers},
   JOURNAL = {Ann. Statist.},
  FJOURNAL = {The Annals of Statistics},
    VOLUME = {35},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {608--633},
      ISSN = {0090-5364},
     CODEN = {ASTSC7},
   MRCLASS = {62H30 (62G07 62G08 62H05)},
  MRNUMBER = {MR2336861},
  }
  

%%%%

@book {Mas:2003:St-Flour,
    AUTHOR = {Massart, Pascal},
     TITLE = {Concentration inequalities and model selection},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {1896},
      NOTE = {Lectures from the 33rd Summer School on Probability Theory
              held in Saint-Flour, July 6--23, 2003},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2007},
     PAGES = {xiv+337},
      ISBN = {978-3-540-48497-4; 3-540-48497-3},
   MRCLASS = {62-02 (60E15 62B10 62G05 62G07 62G30 94A17)},
  MRNUMBER = {MR2319879},
}

@article{Efr:1983,
    AUTHOR = {Efron, Bradley},
     TITLE = {Estimating the error rate of a prediction rule: improvement on cross-validation},
   JOURNAL = {J. Amer. Statist. Assoc.},
  FJOURNAL = {Journal of the American Statistical Association},
    VOLUME = {78},
      YEAR = {1983},
    NUMBER = {382},
     PAGES = {316--331},
      ISSN = {0162-1459},
     CODEN = {JSTNAL},
   MRCLASS = {62F10},
  MRNUMBER = {MR711106 (84k:62039)},
}

@Article{vc-ucrfep-71,
  author = {Vladimir N. Vapnik and A. Y. Chervonenkis},
   title = {On the uniform convergence of relative frequencies of events to their probabilities},
 journal = {Theory of Probability and its Applications},
  volume = {16},
  number = {2},
    year = {1971},
   pages = {264--280},
}