Title: Jackknife, small bandwidth and high-dimensional asymptotics
Authors: Yukitoshi Matsushita - Hitotsubashi University (Japan)
Taisuke Otsu - London School of Economics (United Kingdom) [presenting]
Abstract: Light is shed on problems of statistical inference under alternative or nonstandard 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 semiparametric 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 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.