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Uniform Inference in High-Dimensional Generalized Additive Models
Apr 03, 2020
We develop a method for uniform valid confidence bands of a nonparametric component $f_1$ in the general additive model $Y=f_1(X_1)+\ldots + f_p(X_p) + \varepsilon$ in a high-dimensional setting. We employ sieve estimation and embed it in a high-dimensional Z-estimation framework allowing us to construct uniformly valid confidence bands for the first component $f_1$. As usual in high-dimensional settings where the number of regressors $p$ may increase with sample, a sparsity assumption is critical for the analysis. We also run simulations studies which show that our proposed method gives reliable results concerning the estimation properties and coverage properties even in small samples. Finally, we illustrate our procedure with an empirical application demonstrating the implementation and the use of the proposed method in practice.
Transformation Models in High-Dimensions
Dec 20, 2017
Transformation models are a very important tool for applied statisticians and econometricians. In many applications, the dependent variable is transformed so that homogeneity or normal distribution of the error holds. In this paper, we analyze transformation models in a high-dimensional setting, where the set of potential covariates is large. We propose an estimator for the transformation parameter and we show that it is asymptotically normally distributed using an orthogonalized moment condition where the nuisance functions depend on the target parameter. In a simulation study, we show that the proposed estimator works well in small samples. A common practice in labor economics is to transform wage with the log-function. In this study, we test if this transformation holds in CPS data from the United States.