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Abstract for:

Local M-estimation with discontinuous criterion for dependent and limited observations

Myung  Hwan Seo,  Taisuke  Otsu,  October 2016
Paper No' EM/589: | Full paper (pdf)
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Keywords: Cube root asymptotics, Maximal inequality, Mixing process, Partial identification, Parameter-dependent localization

JEL Classification: C12; C14

Is hard copy/paper copy available? YES - Paper Copy Still In Print.
This Paper is published under the following series: Econometrics
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Abstract:

This paper examines asymptotic properties of local M-estimators under three sets of high-level conditions. These conditions are sufficiently general to cover the minimum volume predictive region, conditional maximum score estimator for a panel data discrete choice model, and many other widely used estimators in statistics and econometrics. Specifically, they allow for discontinuous criterion functions of weakly dependent observations, which may be localized by kernel smoothing and contain nuisance parameters whose dimension may grow to infinity. Furthermore, the localization can occur around parameter values rather than around a fixed point and the observation may take limited values, which leads to set estimators. Our theory produces three different nonparametric cube root rates and enables valid inference for the local M-estimators, building on novel maximal inequalities for weakly dependent data. Our results include the standard cube root asymptotics as a special case. To illustrate the usefulness of our results, we verify our conditions for various examples such as the Hough transform estimator with diminishing bandwidth, maximum score-type set estimator, and many others.