Introduction to Empirical Processes and Semiparametric Inference

Overview.- An Overview of Empirical Processes.- Overview of Semiparametric Inference.- Case Studies I.- Empirical Processes.- to Empirical Processes.- Preliminaries for Empirical Processes.- Stochastic Convergence.- Empirical Process Methods.- Entropy Calculations.- Bootstrapping Empirical Processes.- Additional Empirical Process Results.- The Functional Delta Method.- Z-Estimators.- M-Estimators.- Case Studies II.- Semiparametric Inference.- to Semiparametric Inference.- Preliminaries for Semiparametric Inference.- Semiparametric Models and Efficiency.- Efficient Inference for Finite-Dimensional Parameters.- Efficient Inference for Infinite-Dimensional Parameters.- Semiparametric M-Estimation.- Case Studies III.

[1]  R. Kanwal.  Linear Integral Equations , 1925, Nature.

[2]  J. Dugundji.  An extension of Tietze's theorem. , 1951 .

[3]  M. Donsker.  Justification and Extension of Doob's Heuristic Approach to the Kolmogorov- Smirnov Theorems , 1952 .

[4]  J. Kiefer,et al.  Asymptotic Minimax Character of the Sample Distribution Function and of the Classical Multinomial Estimator , 1956 .

[5]  U. Grenander.  On the theory of mortality measurement , 1956 .

[6]  V. P. Godambe.  An Optimum Property of Regular Maximum Likelihood Estimation , 1960 .

[7]  V. Strassen.  An invariance principle for the law of the iterated logarithm , 1964 .

[8]  B. Efron.  The two sample problem with censored data , 1967 .

[9]  Prakasa Rao.  Estimation of a unimodal density , 1969 .

[10]  G. Jameson.  Topology and Normed Spaces , 1974 .

[11]  P. Major,et al.  An approximation of partial sums of independent RV'-s, and the sample DF. I , 1975 .

[12]  L. J. Wei,et al.  The Adaptive Biased Coin Design for Sequential Experiments , 1978 .

[13]  R. Koenker,et al.  Asymptotic Theory of Least Absolute Error Regression , 1978 .

[14]  Richard M. Dudley,et al.  Invariance principles for sums of Banach space valued random elements and empirical processes , 1983 .

[15]  Eric V. Slud,et al.  Sequential Linear Rank Tests for Two-Sample Censored Survival Data , 1984 .

[16]  P. Groeneboom.  Brownian motion with a parabolic drift and airy functions , 1989 .

[17]  R. C. Bradley.  Basic Properties of Strong Mixing Conditions , 1985 .

[18]  J. Lindenstrauss,et al.  Extensions of lipschitz maps into Banach spaces , 1986 .

[19]  Ernst Eberlein,et al.  Dependence in probability and statistics : a survey of recent results (Oberwolfach, 1985) , 1988 .

[20]  Donald W. K. Andrews,et al.  An empirical process central limit theorem for dependent non-identically distributed random variables , 1989 .

[21]  H. Künsch.  The Jackknife and the Bootstrap for General Stationary Observations , 1989 .

[22]  M. Taqqu,et al.  The Empirical Process of some Long-Range Dependent Sequences with an Application to $U$-Statistics , 1989 .

[23]  P. Massart.  The Tight Constant in the Dvoretzky-Kiefer-Wolfowitz Inequality , 1990 .

[24]  Myron N. Chang.  Weak Convergence of a Self-Consistent Estimator of the Survival Function with Doubly Censored Data , 1990 .

[25]  D. Pollard,et al.  Cube Root Asymptotics , 1990 .

[26]  D. Pollard.  Empirical Processes: Theory and Applications , 1990 .

[27]  D. Pollard.  Asymptotics for Least Absolute Deviation Regression Estimators , 1991, Econometric Theory.

[28]  Tze Leung Lai,et al.  Weak Convergence of Time-Sequential Censored Rank Statistics with Applications to Sequential Testing in Clinical Trials , 1991 .

[29]  Regina Y. Liu.  Moving blocks jackknife and bootstrap capture weak dependence , 1992 .

[30]  Raul Cano.  On The Bayesian Bootstrap , 1992 .

[31]  M. Chavance.  [Jackknife and bootstrap]. , 1992, Revue d'epidemiologie et de sante publique.

[32]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[33]  P. Bickel.  Efficient and Adaptive Estimation for Semiparametric Models , 1993 .

[34]  J. Wellner,et al.  Exchangeably Weighted Bootstraps of the General Empirical Process , 1993 .

[35]  Joseph P. Romano,et al.  Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions , 1994 .

[36]  M. A. Arcones,et al.  Central limit theorems for empirical andU-processes of stationary mixing sequences , 1994 .

[37]  Bin Yu.  RATES OF CONVERGENCE FOR EMPIRICAL PROCESSES OF STATIONARY MIXING SEQUENCES , 1994 .

[38]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

[39]  U. V. Naik-Nimbalkar,et al.  Validity of blockwise bootstrap for empirical processes with stationary observations , 1994 .

[40]  W. Polonik.  Measuring Mass Concentrations and Estimating Density Contour Clusters-An Excess Mass Approach , 1995 .

[41]  P. Bühlmann.  The blockwise bootstrap for general empirical processes of stationary sequences , 1995 .

[42]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[43]  D. Radulovic.  The bootstrap for empirical processes based on stationary observations , 1996 .

[44]  Sara van de Geer,et al.  Penalized quasi-likelihood estimation in partial linear models , 1997 .

[45]  E. Mammen.  The Bootstrap and Edgeworth Expansion , 1997 .

[46]  .. W. V. Der,et al.  On Profile Likelihood , 2000 .

[47]  M. Peligrad,et al.  ON THE BLOCKWISE BOOTSTRAP FOR EMPIRICAL PROCESSES FOR STATIONARY SEQUENCES , 1998 .

[48]  Robert E. Megginson.  An Introduction to Banach Space Theory , 1998 .

[49]  M. Kosorok.  Two-sample quantile tests under general conditions , 1999 .

[50]  S. R. Jammalamadaka,et al.  Empirical Processes in M-Estimation , 2001 .

[51]  Herold Dehling,et al.  Empirical Process Techniques for Dependent Data , 2002 .

[52]  J. Dedecker,et al.  Maximal Inequalities and Empirical Central Limit Theorems , 2002 .

[53]  Empirical Processes of Long-memory Sequences , 2003 .

[54]  Michael R. Kosorok,et al.  Bootstraps of sums of independent but not identically distributed stochastic processes , 2003 .

[55]  Michael R. Kosorok,et al.  Temporal process regression , 2004 .

[56]  B. Ripley,et al.  Robust Statistics , 2018, Wiley Series in Probability and Statistics.

[57]  Michael R. Kosorok,et al.  FURTHER DETAILS ON INFERENCE UNDER RIGHT CENSORING FOR TRANSFORMATION MODELS WITH A CHANGE-POINT BASED ON A COVARIATE THRESHOLD , 2006, math/0604043.

[58]  Xiongzhi Chen.  Brownian Motion and Stochastic Calculus , 2008 .