EMPIRICAL PROCESSES WORKING GROUP

Winter and Spring Quarters, 2001

Primary References for Spring 2001:

• Van der Vaart, A. W. (2000).
  Semiparametric Statistics.
  Lectures on Probability Theory, Ecole d'Ete de Probabilites de St. Flour XX??- 1999,
  P. Bernard, Ed. Springer, Berlin; to appear.
• Rio, E. (2000).
  Inégalités exponentielles pour les processus empiriques.
  C. R. Acad. Sci. Paris 330, 597-600.
• Panchenko, D. (2001).
  A note on Talagrand's concentration inequality for empirical processes.
  Technical Report, University of New Mexico.
• Massart, P. (2000).
  About the constants in Talagrand's concentration inequalities for empirical processes.
  Annals of Probability 28, 863-884.

Primary References for Winter 2001:

• Van der Vaart, A. W., and Wellner, J. A. (2000).
  Weak Convergence and Empirical Processes,
  Corrected second printing. Springer-Verlag, New York.
  
• Van der Vaart, A. W. (2000).
  Semiparametric Statistics.
  Lectures on Probability Theory, Ecole d'Ete de Probabilites de St. Flour XX??- 1999,
  P. Bernard, Ed. Springer, Berlin; to appear.
• Van de Geer, Sara A. (2000).
  Empirical Processes in M-Estimation, Cambridge University Press, Cambridge.
• Dudley, R. M. (1999).
  Uniform Central Limit Theorems, Cambridge University Press, Cambridge.
• de la Pena, V. H. and Gine, Evarist (1999).
  Decoupling: From Dependence to Independence, Springer, New York.
• Pollard, D. (1990).
  Empirical Processes: Theory and Applications, IMS, Hayward

Miscellaneous Notes:

• An application of empirical process theory.
• Notes on Entropy Numbers.
• Notes on Exponential Bounds.
• Notes on the Huber-Pollard Z-theorem.
• Preservation Theorems for Glivenko-Cantelli classes.
• Chapter 2.2 Notes by Hao Liu; posted 1/11/01.

A Selection of Other Books and Papers about Empirical Processes

Basic Empirical Process Literature:

• Dudley, R. M. (1978). Central limit theorems for empirical measures. Annals of Probability 6, 899 929. Correction: Ann. Probability 7, 909 - 911.
• Dudley, R. M. (1984). A course on empirical processes; École d'Été de Probabilités de Saint-Flour XII-1982. Lecture Notes in Mathematics 1097, 2 - 141. Springer-Verlag, New York.
• Giné, E. and Zinn, J. (1984). Some limit theorems for empirical processes. Annals of Probability 12, 929 - 989.
• Dudley, R. M. (1987). Universal Donsker classes and metric entropy. Ann. Probability 15, 1306-1326.
• Pollard, D. (1984). Convergence of Stochastic Processes. Springer-Verlag, New York.
• Pollard, D. (1990). Empirical Processes: Theory and Applications. NSF-CBMS Regional Conference Series in Probability and Statistics, Volume 2, Society for Industrial and Applied Mathematics, Philadelphia. Institute of Mathematical Statistics and American Statistical Association, Hayward.
• Giné, E., and Zinn, J. (1986). Lectures on the central limit theorem for empirical processes. Lecture Notes in Mathematics 1221, 50 -113. Springer-Verlag, New York.
• Shorack, G. R. and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics, Wiley, New York.
• Van der Vaart, A. W., and Wellner, J. A. (1996). Weak Convergence and Empirical Processes, Springer-Verlag, New York.

Applications of Empirical Processes in Statistics

Basic M- and Z- Estimator Theorems:

• Huber, P. J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. Proc. Fifth Berkeley Symp. Math. Statist. Prob. 1, 221 - 233. Univ. California Press.
• Pollard, D. (1985). New ways to prove central limit theorems. Econometric Theory 1, 295 - 314.
• Pakes, A. and Pollard, D. (1989). Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027 - 1057.
• Kim, J. and Pollard, D. (1990). Cube root asymptotics. Ann. Statist. 18, 191 - 219.
• Nolan, D. (1991). The excess-mass ellipsoid. J. Mult. Anal. 39, 348 - 371.
• Huang, J. (1993). Central limit theorems for M-estimates. Technical Report 251, Department of Statistics, University of Washington.

Infinite-Dimensional M- and Z- Estimator Theorems:

• Gill, R. D. (1989). Non- and semi-parametric maximum likelihood estimators and the von-Mises method - I. Scan. J. Statist. 16, 97 - 128.
• Gill, R. D. and Van der Vaart, A. W. (1993). Non- and semi-parametric maximum likelihood estimators and the von-Mises method - II. Scan. J. Statist. 20, 271 - 288.
• Van der Vaart, A. W. (1995a). Efficiency of infinite dimensional M-estimators. Statistica Neerl. 49, 9 - 30.

Bootstrapping M- and Z- Estimators:

• Arcones, M. A. and Giné, E. (1992). On the bootstrap of M - estimators and other statistical functionals. Exploring the Limits of Bootstrap, 14 - 47. Wiley, New York. R. LePage and L. Billard, editors.
• Wellner, J. A. and Zhan, Y. (1996). Bootstrapping infinite-dimensional Z- estimators. Submitted to Bernoulli.
• Zhan, Y. (1996). Bootstrapping Functional M-estimators. Unpublished Ph.D. dissertation, University of Washington.

Rates of Convergence in Nonparametric Estimation via Empirical Processes:

• Birgé, L. and Massart, P. (1993). Rates of convergence for minimum contrast estimators. Probability Theory and Related Fields 97, 113 - 150.
• Shen, X., and Wong, W. H. (1994). Convergence rate of sieve estimates. Ann. Statist. 22, 580-615.
• Van de Geer, S. (1993). Hellinger-consistency of certain nonparametric maximum likelhood estimators. Ann. Statist. 21, 14 - 44.
• Wong, W. H., and Shen, X. (1995). Probability inequalities for likelihood ratios and convergence rates of sieve MLE's. Ann. Statist. 23, 339 - 363.

Recent Literature Using Empirical Process Methods in Semiparametric and NonparametricModels:

• Emond, M. J. and Self, S. (1993). An efficient estimator for the generalized semilinear model. J. Amer. Statist. Assoc. 92, 1033-1040.
• Gilbert, P. (1996). Semiparametric biased sampling models. Submitted to Ann. Statist.
• Geskus, R. and Groeneboom, P. (1997). Asymptotically optimal estimation of smooth functionals for interval censoring, case 2. Technical Report, Delft University. Submitted to Ann. Statist.
• Huang, J. (1996). Efficient estimation for the Cox model with interval censoring. Ann. Statist. 24, 540-568.
• Mammen, E. and Van de Geer, S. (1997). Penalized quasi-likelihood estimation in partial linear models. Ann. Statist. 25, 1014-1035.
• Murphy, S. A. (1995). Asymptotic theory for the frailty model. Ann. Statist. 23, 182-198.
• Murphy, S. A. and Van der Vaart, A.W. (1995). Semiparametric likelihood ratio inference. Ann. Statist. 25, 1471 - 1509.
• Parner, E. (1998). Asymptotic theory for the correlated gamma-frailty model. Ann. Statist. 26, 183 - 214.
• Van der Vaart, A. W. (1994). Maximum likelihood estimation with partially censored data. Ann. Statist. 22, 1896 - 1916.
• Van der Vaart, A. W. (1996). Efficient maximum likelihood estimation in semiparametric mixture models. Ann. Statist. 24, 862-878.
• Van der Vaart, A. W. (2000). Semiparametric Statistics. Lectures on Probability Theory., Ecole d'Ete de Probailites de St. Flour XX??- 1999, Ed. P. Bernard. Springer, Berlin; to appear.
• Wellner, J. A. and Zhang, Y. (1998). Large sample theory for an estimator of the mean of a counting process with panel count data. Technical Report No. 327, Department of Statistics, University of Washington. Submitted to Ann. Statist.