Invites you to a

Econometrics seminar presented by

Nan Zou

(Macquarie University)

Bootstrap Massive

Joint with Patrice Bertail, Dimitris Politis and Stanislav Volgushev

&

Chaotic Data

Joint with Kasun Fernando

Wednesday 24 August

2.00pm – 3.30pm

Via Zoom: Meeting Link

Abstract: This talk contains two parts. Its first part investigates the “bag of little bootstraps”, a bootstrap designed for massive data. In classic statistical inference, the bootstrap stands out as a simple, powerful, and data-driven technique. However, when coping with massive data sets, which are increasingly prevalent these days, the bootstrap can be computationally infeasible. To speed up the bootstrap for massive data sets, the bag of little bootstraps has been invented in 2014. Despite its considerable popularity, little is known about the bag of little bootstraps’s theoretical properties, including reliability. Indeed, our preliminary results have already raised questions on the applicability of the bag of little bootstraps under a simple but important setting. This part will first introduce the bag of little bootstraps procedure and then investigate its theoretical applicability. Specifically, for this applicability, this part will present a counterexample for the claimed sufficient condition in the literature and will, as a remedy, provide a hopefully correct, generic sufficient condition. This part is joint with P. Bertail, D. Politis, and S. Volgushev

This talk’s second part introduces the bootstrap for chaotic dynamical systems. After its establishment in the late 19th century through the efforts of Poincaré (1879) and Lyapunov (1892), the theory of dynamical systems was applied to study processes that change over time. Despite their deterministic nature, dynamical systems can exhibit incomprehensibly chaotic behaviors and seemingly random patterns. Consequently, a dynamical system is usually represented by a probabilistic model, in which the unknown parameters must be estimated using statistical methods. To measure the uncertainty of such estimation, we develop a bootstrap method and establish its consistency and second-order efficiency via continuous Edgeworth expansions. This part is joint with K. Fernando.

For further information contact: Econometrics seminar series coordinator Dr Ye Lu (ye.lu1@sydney.edu.au)

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