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Jackknife, small bandwidth and high-dimensional asymptotics - Regular Dept Seminar

Wednesday 13 November 2019, 1.00PM to 2.00 pm

Speaker(s): Tai Otsu (LSE)

Hosts: Francesco Bravo & Takashi Yamagata

1:1 meetings: doodle poll

Abstract: This paper sheds light on problems of statistical inference under alternative or non- standard asymptotic frameworks from the perspective of jackknife empirical likelihood (JEL). Examples include small bandwidth asymptotics for semiparametric inference, many covariates asymptotics for regression models, and many-weak instruments asymptotics for instrumental variable regression. We first establish Wilks’ theorem for the JEL statistic on a general semi- parametric inference problem under the conventional asymptotics. We then show that the JEL statistics lose asymptotic pivotalness under the above nonstandard asymptotic frameworks, and argue that these phenomena are understood as emergence of Efron and Stein’s (1981) bias of the jackknife variance estimator in the first order. Finally we propose a modification of JEL to recover asymptotic pivotalness under both the conventional and nonstandard asymptotics. Our modification works for all above examples and provides a unified framework to investigate nonstandard asymptotic problems. 

Jackknife, small bandwidth and high-dimensional asymptotics (PDF , 465kb) 

Location: A/RC/014

Admission: All welcome