Collaborative Research: Small Bandwidth Asymptotic Theory for Kernel-Based Semiparametric Estimators

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Statistical models in social and natural sciences typically include a parameter of interest as well as other parameters that need to be estimated (nuisance parameters) using the data available to the researcher. Among these models, the so-called semiparametric models are of particular importance because they are flexible and less sensitive to biases generated by model misspecification. Because the nuisance parameters in these models are unknown functions, researchers use nonparametric techniques in their estimation and usually rely on asymptotic theory (approximations that assume a large amount of data) to conduct statistical inference. Although classical asymptotic theory for semiparametric estimators is well developed, these results are in general not robust to departures from the underlying assumptions imposed. Moreover, the applicability of semiparametric estimators is often limited by the sensitivity of their performance to seemingly ad hoc choices of smoothing and tuning parameters involved in the estimation procedure. This lack of robustness usually translates in incorrect statistical inference that may lead researchers and policy-makers to draw flawed conclusions from empirical work that employs these semiparametric estimators.As a consequence, it is crucial to investigate whether it is possible to conduct statistical inference using semiparametric estimators that is robust to changes in the tuning and smoothing parameters choices underlying the nonparametric estimator, and to departures from the unobservable assumptions underlying the semiparametric model. This project seeks to provide non-standard asymptotic theory for a class of semiparametric estimators that allows for robust statistical inference. The main focus of this project is on a particular, yet important, semiparametric estimator called the density-weighted average derivative estimator. Preliminary findings obtained for this estimator, show that our proposed non-standard asymptotic theory provides the basis for the construction of statistical procedures that exhibit certain forms of robustness that may be appealing from both theoretical and empirical perspectives. This proposal also discusses how this theory affects the validity of commonly used resampling procedures, how tuning parameters may be selected in applications (while being consistent with our non-standard asymptotics), and whether this idea may be applied more broadly to other semiparametric estimators. The results of this research are expected to benefit several fields of study, ranging from Economics or Political Science to Biostatistics or Public Health, allowing researchers to conduct robust inference in semiparametric models, and making semiparametric inference more attractive to researchers and policy-makers.