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1. The fast iterated bootstrap

Author

Mirza Trokic, Russell Davidson, McGill University = Université McGill [Montréal, Canada], Centre interuniversitaire de recherche en économie quantitative (CIREQ), Aix-Marseille Sciences Economiques (AMSE), École des hautes études en sciences sociales (EHESS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), IHS Markit, and This research was supported by the Canada Research Chair program (Chair in Economics, McGill University), and by grants from the Social Sciences and Humanities Research Council of Canada and the Fonds de Recherche du QuebecSociete Culture, Canada. We are grateful to seminar participants at the Third French Econometric Conference, the Singapore Management University, the Hong Kong University of Science and Technology, and the University of Sydney, for useful comments. We also thank our discussant Matt Webb for insightful comments at the 2017 CESG. Our thanks go to three anonymous referees and a guest co-editor for insightful comments that helped us improve the paper.

Subjects
Economics and Econometrics, Series (mathematics), Computer science, Applied Mathematics, 05 social sciences, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C12 - Hypothesis Testing: General, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C10 - General, Sense (electronics), [SHS.ECO]Humanities and Social Sciences/Economics and Finance, 01 natural sciences, Power (physics), Bootstrap iteration Fast iterated bootstrap, 010104 statistics & probability, JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C63 - Computational Techniques • Simulation Modeling, Null (SQL), Iterated function, Distortion, 0502 economics and business, bootstrap iteration, fast iterated bootstrap, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C15 - Statistical Simulation Methods: General, 0101 mathematics, Algorithm, 050205 econometrics
Abstract

International audience; The standard forms of bootstrap iteration are very computationally demanding. As a result, there have been several attempts to alleviate the computational burden by use of approximations. In this paper, we extend the fast double bootstrap of Davidson and MacKinnon (2007) to higher orders of iteration, and provide algorithms for their implementation. The new methods make computational demands that increase only linearly with the level of iteration, unlike standard procedures, whose demands increase exponentially. In a series of simulation experiments, we show that the fast triple bootstrap improves on both the standard and fast double bootstraps, in the sense that it suffers from less size distortion under the null with no accompanying loss of power.

Published
2020
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2. Maximum Distortion Attacks in Electricity Grids

Author

H. Vincent Poor, Oliver Kosut, Inaki Esnaola, Samir M. Perlaza, University of Sheffield [Sheffield], Software and Cognitive radio for telecommunications (SOCRATE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-CITI Centre of Innovation in Telecommunications and Integration of services (CITI), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA), Princeton University, Arizona State University [Tempe] (ASU), This work was supported in part by the European Commission under Individual Fellowship Marie Skłodowska-CurieAction (CYBERNETS) under Grant 659316, and in part by the U.S. National Science Foundation under Grant CMMI-1435778 and Grant ECCS-1549881. Paper no. TSG-01065-2015., European Project: 659316,H2020 Pilier Excellent Science,H2020-MSCA-IF-2014,CYBERNETS(2015), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), and Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon

Subjects
game theory, State variable, Mathematical optimization, Data-injection attacks, General Computer Science, Exploit, MMSE estimation, 020209 energy, [MATH.MATH-IT]Mathematics [math]/Information Theory [math.IT], 020206 networking & telecommunications, 02 engineering and technology, symbols.namesake, Cardinality, de-centralized attacks, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Nash equilibrium, Distortion, 0202 electrical engineering, electronic engineering, information engineering, symbols, Potential game, Game theory, Gaussian process, Mathematics, Computer Science::Cryptography and Security
Abstract

International audience; Multiple attacker data injection attack construction in electricity grids with minimum-mean-square-error state estimation is studied for centralized and decentralized scenarios. A performance analysis of the trade-off between the maximum distortion that an attack can introduce and the probability of the attack being detected by the network operator is considered. In this setting, optimal centralized attack construction strategies are studied. The decentralized case is examined in a game-theoretic setting. A novel utility function is proposed to model this trade-off and it is shown that the resulting game is a potential game. The existence and cardinality of the corresponding set of Nash Equilibria (NEs) of the game is analyzed. Interestingly, the attackers can exploit the correlation among the state variables to facilitate the attack construction. It is shown that attackers can agree on a data injection vector construction that achieves the best trade-off between distortion and detection probability by sharing only a limited number of bits offlline. For the particular case of two attackers, numerical results based on IEEE test systems are presented.

Published
2016
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