Asymptotic Statistics
Abstract
This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.
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Under mild moment conditions, the requirements of Assumptions A.1-A.2 are fulfilled when one adopts linear/nonlinear outcome regressions or logit/probit models and estimates the unknown parameters by nonlinear least squares, quasi-maximum likelihood, or other alternative estimation methods.
“Under mild moment conditions, these requirements are fulfilled when one adopts linear/nonlinear outcome regressions or logit/probit models, for example, and estimates the unknown parameters by (nonlinear) least squares, quasi-maximum likelihood, or other alternative estimation methods”
From Doubly robust difference-in-differences estimators (2020) · cites this paper as van der Vaart (1998)
Under mild moment conditions, the requirements of Assumptions 7-8 are fulfilled when one adopts linear/nonlinear outcome regressions or logit/probit models, and estimates unknown parameters by nonlinear least squares, quasi-maximum likelihood, or other alternative estimation methods.
“Under mild moment conditions, these requirements are fulfilled when one adopts linear/nonlinear outcome regressions or logit/probit models, for example, and estimates the unknown parameters by (nonlinear) least squares, quasi-maximum likelihood, or other alternative estimation methods, see e.g. Chapter 5 in van der Vaart (1998), Wooldridge (2007), Graham et al. (2012) and Sant'Anna and Zhao (2020)”
From Difference-in-Differences with multiple time periods (2021) · cites this paper as van der Vaart (1998)
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Sorted by citations
Difference-in-Differences with multiple time periods
Callaway, B., & Sant’Anna, P. H. C. (2021) · Journal of Econometrics · doi:10.1016/j.jeconom.2020.12.001 · Cited by 9,126 · see citing works
Semiparametric Difference-in-Differences Estimators
Abadie, A. (2005) · The Review of Economic Studies · doi:10.1111/0034-6527.00321 · Cited by 2,286 · see citing works
Estimation of prediction error by using K-fold cross-validation
Fushiki, T. (2011) · Statistics and Computing · doi:10.1007/s11222-009-9153-8 · Cited by 1,470 · see citing works
Machine Learning Methods That Economists Should Know About
Athey, S., & Imbens, G. W. (2019) · Annual Review of Economics · doi:10.1146/annurev-economics-080217-053433 · Cited by 1,163 · see citing works
Identification and Inference in Nonlinear Difference-in-Differences Models
Athey, S., & Imbens, G. W. (2006) · Econometrica · doi:10.1111/j.1468-0262.2006.00668.x · Cited by 1,084 · see citing works
Doubly robust difference-in-differences estimators
Sant’Anna, P. H. C., & Zhao, J. (2020) · Journal of Econometrics · doi:10.1016/j.jeconom.2020.06.003 · Cited by 1,047 · see citing works
Murphy, S. A., & Van Der Vaart, A. W. (2000) · Journal of the American Statistical Association · doi:10.1080/01621459.2000.10474219 · Cited by 712 · see citing works
Inference on Counterfactual Distributions
(2013) · Econometrica · doi:10.3982/ecta10582 · Cited by 601 · see citing works
Program evaluation and causal inference with high-dimensional data
Belloni, A., Chernozhukov, V., Fern�ndez-Val, I., & Hansen, C. (2017) · Econometrica · doi:10.3982/ecta12723 · Cited by 317 · see citing works
Survivor bias in Mendelian randomization analysis
Vansteelandt, S., Dukes, O., & Martinussen, T. (2018) · Biostatistics · doi:10.1093/biostatistics/kxx050 · Cited by 46 · see citing works
Efficient Tests Under a Weak Convergence Assumption
(2011) · Econometrica · doi:10.3982/ecta7793 · Cited by 30 · see citing works
Online Non-Negative Convolutive Pattern Learning for Speech Signals
Wang, D., Vipperla, R., Evans, N., & Zheng, T. F. (2013) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2012.2222381 · Cited by 25 · see citing works
- Authors
- Vaart, A. W. V. D.
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 1998-10-13
- OpenAlex
- W1460189015
- Cited by
- 4,159
- References
- 0
- Citations by year
- 2026: 208 · 2025: 283 · 2024: 257 · 2023: 226 · 2022: 278 · 2021: 275 · 2020: 220 · 2019: 209 · 2018: 221 · 2017: 207 · 2016: 169 · 2015: 184 · 2014: 212 · 2013: 168 · 2012: 176
- FWCI
- 4.10
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- asymptotic statistics, likelihood-based inference, M-estimation, asymptotic efficiency, U-statistics, semiparametric models, bootstrapping, empirical processes
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