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Inference for Semi-Nonparametric Econometric Models

Final Report Summary - SNP (Inference for Semi-Nonparametric Econometric Models)

This research project aims to contribute for advances in the research on semiparametric and nonparametric econometric methods by developing novel estimation and inference approaches in a variety of contexts and applying them to important empirical problems in economics.
The major achievements of the project are categorized into two parts. First, robust inference methods in mathematics and statistics are extended to substantial challenges in econometric modeling. Starting from a paper on robust inference for moment condition models, various robust inference methods, especially against measurement errors, are developed for instrumental variable regression, specification testing, distribution functions, additive models, for average derivatives, density estimation, and varying coefficient models. Also, the project developed a nonparametric technique for extremal tail events and robust estimation method for monotone index models.
Second, the fundamental concept of likelihood in data science and related inference methods are extended to various challenges from new data environments. In particular, various empirical likelihood methods are developed for random sets, average derivatives, regression discontinuity designs, high frequency data, generated variable problems, and missing data models. Furthermore, several novel likelihood concepts are developed for cube root asymptotic problems, modified likelihood for panel data models, relative error correct inference via saddlepoint approximation, high-dimensional models via information theoretic approach, and general non-standard asymptotic problems.
In the entire lifetime of the project, 24 papers are completed. All papers were submitted to major international journals in economics, econometrics, and statistics. Twelve of them have been already published or accepted for publication (including the Journal of Econometrics, Econometric Theory, Annals of Statistics, and Journal of the American Statistical Association), other four are at the revise and resubmission stage, and remaining eight are under review or initial submission stage.