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Econometrics Workshop: Kengo Kato

Tuesday, October 16, 2018 at 11:40am to 1:10pm

Uris Hall, 498

Kengo Kato - Cornell University, Statistics Department

Jackknife Multiplier Bootstrap: Finite Sample Approximations to the U-process Supremum with Applications (joint w/Xiaohui Chen)

Abstract: In this talk, I will discuss finite sample approximations to the supremum of a non-degenerate U-process of a general order indexed by a function class. We are primarily interested in situations where the function class as well as the underlying distribution change with the sample size, and the U-process itself is not weakly convergent as a process. Such situations arise in a variety of modern statistical problems. We first consider Gaussian approximations, namely, approximate the U-process supremum by the supremum of a Gaussian process, and derive coupling and Kolmogorov distance bounds. Such Gaussian approximations are, however, not often directly usable in statistical problems since the covariance function of the approximating Gaussian process is unknown. This motivates us to study bootstrap-type approximations to the U-process supremum. We propose a novel jackknife multiplier bootstrap (JMB) tailored to the U-process, and derive coupling and Kolmogorov distance bounds for the proposed JMB method. All these results are non-asymptotic, and established under fairly general conditions on function classes and underlying distributions. Key technical tools in the proofs are new local maximal inequalities for U-processes, which may be useful in other contexts. We also discuss applications of the general approximation results to testing for qualitative features of nonparametric functions based on generalized local U-processes.

Event Type

Class/ Workshop

Departments

Economics

Tags

economics, EconSeminar, EconMetrics

Hashtag

#CornellEcon

Contact E-Mail

alg5@cornell.edu

Contact Name

Amy Moesch

Contact Phone

607-255-5617

Speaker

Kengo Kato

Speaker Affiliation

Cornell University

Open To

Cornell Economics Community (List Serve Members)

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