Essays in Transformation Models PDF Download

Author: Jian Zhang
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Languages : en
Pages : 0

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Book Description
In Chapter 1, I study the estimation and inference of transformation models in the presence of a high dimensional set of control variables. In the study, I consider a generalized form of the transformed model, which includes the traditional transformed model, binary choice model, and generalized accelerated failure time model as special cases. I include both low dimensional covariates of interest and high dimensional control variables in this model. The estimation of high dimension nuisance parameters could lead to substantial bias and thus incorrect inference on parameters of interest. I provide a double-machine learning estimator to reduce this substantial bias and obtain a root-n-consistent and asymptotically normal results. According to the simulation study, I compare the performance of our estimator with the classical estimator based on average partial derivatives, it turns out that our estimator has less bias and provides correct inference results. Finally, I use an empirical example to illustrate the performance of our estimator in real data. In Chapter 2, I study the specification test for a generalized additive model (a.k.a. GAM) with an unknown link function. GAM is widely used to reduce the curse of dimensionality in nonparametric estimation. Additive Model is a special case when the link function is known by econometricians to be an identity. Under some regular conditions, I derive a sufficient and necessary condition when a function can be written as a GAM, which turns out to be a partial differential equation. This equation implies countably many restrictions on the coefficients from a simple polynomial series estimation, which forms the base of our test. Therefore, our test doesn't need to run a GAM estimation. Instead, I use an ``unrestricted'' series regression estimation with polynomial basis functions and make a statistical inference on its coefficients. The asymptotic properties of the test statistics are derived. The asymptotic distribution is the Chi-squared distribution with an increasing degree of freedom. A Monte Carlo study is shown for the case with two variables.