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Essays in robust estimation and inference in semi- and nonparametric econometrics

Abstract : In the introductory chapter, we compare views on estimation and inference in the econometric and statistical learning disciplines.In the second chapter, our interest lies in a generic class of nonparametric instrumental models. We extend the estimation procedure in Otsu (2011) by adding a regularisation term to it. We prove the consistency of our estimator under Lebesgue's L2 norm.In the third chapter, we show that when observations are jointly exchangeable rather than independent and identically distributed (i.i.d), a modified version of the empirical process converges weakly towards a Gaussian process under the same conditions as in the i.i.d case. We obtain a similar result for a modified version of the bootstrapped empirical process. We apply our results to get the asymptotic normality of several nonlinear estimators and the validity of bootstrap-based inference. Finally, we revisit the empirical work of Santos Silva and Tenreyro (2006).In the fourth chapter, we address the issue of conducting inference on ratios of expectations. We find that when the denominator tends to zero slowly enough when the number of observations n increases, bootstrap-based inference is asymptotically valid. Secondly, we complement an impossibility result of Dufour (1997) by showing that whenever n is finite it is possible to construct confidence intervals which are not pathological under some conditions on the denominator.In the fifth chapter, we present a Stata command which implements estimators proposed in de Chaisemartin et d'Haultfoeuille (2018) to measure several types of treatment effects widely studied in practice.
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Yannick Guyonvarch. Essays in robust estimation and inference in semi- and nonparametric econometrics. Statistics Theory [stat.TH]. Université Paris-Saclay, 2019. English. ⟨NNT : 2019SACLG007⟩. ⟨tel-02421451⟩

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