Nonparametric regression with nonparametrically generated covariates

By Enno Mammen, Christoph Rothe, Melanie Schienle. 2012

129 citations recorded by the source corpus.

We analyze the properties of non- and semiparametric estimation procedures involving nonparametric regression with generated covariates. Such estimators appear in numerous econometric applications, including nonparametric estimation of simultaneous equation models, sample selection models, treatment effect models, and censored regression models, but so far there seems to be no unified theory to establish their statistical properties. Our paper provides such results, allowing to establish asymptotic properties like rates of consistency or asymptotic normality for a wide range of semi- and nonparametric estimators. We also show how to account for the presence of nonparametrically generated regressors when computing standard errors.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Nonparametric identification and estimation of transformation models (2015, background): “Popular identification restrictions put forth in the literature include the existence of a set of instruments combined with either a mean restriction, as in Newey and Powell (2003), or a median restriction P ( ≤ 0|Z) = 1/2, as in Horowitz and Lee (2007).”
The influence function of semiparametric estimators (2015, background): “This set up generalizes the conditional moment restrictions environment of Newey and Powell (1989, 2003), Newey (1991), and Ai and Chen (2003) to orthogonality conditions with linear restrictions on γ.”
Nonparametric estimation of causal heterogeneity under high-dimensional confounding (2019, background): “Specifically, Hahn and Ridder (2013) (for an alternative theoretical development see also Mammen, Rothe, and Schienle, 2012) investigate a related set-up showing that nonparametric regression on an estimated propensity score can lead to efficient estimation of ATE.”
SEMIPARAMETRIC ESTIMATION WITH GENERATED COVARIATES (2014, methodology): “On the other hand, bounds on the supremum norm of the approximation error, as studied in Mammen et al. (2012), typically vanish at a rate slower than n−1/2, and are thus not useful to establish the “asymptotic normality” condition.”
Nonparametric covariate-adjusted regression (2016, methodology): “Recently, Mammen et al. (2012) gave a deep account of nonparametric estimators computed from nonparametrically generated covariates, but our estimators do not fall into the class of settings they consider, not least because in our case, not only the covariate X, but also the dependent variable Y ,…”
Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regression (2018, methodology): “3 of Negahban et al. (2010), inequality (4.33) implies a rate of convergence if β0 is weakly sparse. Following the proof of Proposition 2 of Negahban et al. (2010), and using the proof of Theorem 4.”
Asymptotic Variance of Semiparametric Estimators With Generated Regressors (2013, background): “This estimator is a special case of that considered in Theorem 6 with h(w; 1; 2) = d p ( 1 2), so that h not only depends on 1; 2, so that the simplication in (7) does not apply.”