IDENTIFICATION AND ESTIMATION OF NONPARAMETRIC STRUCTURAL

This paper concerns a new statistical approach to instrumental variables (IV) method for nonparametric structural models with additive errors. A general identifying condition of the model is proposed, based on richness of the space generated by marginal discretizations of joint density functions. For consistent estimation, we develop statistical regularization theory to solve a random Fredholm integral equation of the first kind. A\ minimal set of conditions are given for consistency of a general regularization method. Using an abstract smoothness condition, we derive some optimal bounds, given the accuracies of preliminary estimates, and show the convergence rates of various regularization methods, including (the ordinary/iterated/generalized) Tikhonov and Showalter's methods. An application of the general regularization theory is discussed with a focus on a kernel smoothing method. We show an exact closed form, as well as the optimal convergence rate, of the kernel IV estimates of various regularization methods. The finite sample properties of the estimates are investigated via a small-scale Monte Carlo experimentNonparametric Strucutral Models, IV estimation, Statistical inverse problems

Korean Jeong (Chŏng) and its relationship to Christian mission

https://place.asburyseminary.edu/ecommonsatsdissertations/1723/thumbnail.jp

A Local Instrumental Variable Estimation Method for Generalized Additive Volatility Models

We investigate a new separable nonparametric model for time series, which includes many ARCH models and AR models already discussed in the literature. We also propose a new estimation procedure based on a localization of the econometric method of instrumental variables. Our method has considerable computational advantages over the competing marginal integration or projection method.ARCH, kernel estimation, nonparametric, volatility.

ESTIMATION OF A SEMIPARAMETRICIGARCH(1,1) MODEL

We propose a semiparametric IGARCH model that allows for persistence invariance but also allows for more flexible functional form. We assume that thedifference of the squared process is weakly stationary. We propose an estimationstrategy based on the nonparametric instrumental variable method. We establishthe rate of convergence of our estimator.Inverse Problem, Instrumental Variable, IGARCH,Kernel Estimation, Nonparametric regression

The live method for generalized additive volatility models.

We investigate a new separable nonparametric model for time series, which includes many autoregressive conditional heteroskedastic (ARCH) models and autoregressive (AR) models already discussed in the literature. We also propose a new estimation procedure called LIVE, or local instrumental variable estimation, that is based on a localization of the classical instrumental variable method. Our method has considerable computational advantages over the competing marginal integration or projection method. We also consider a more efficient two-step likelihood-based procedure and show that this yields both asymptotic and finite-sample performance gains.

Nonparametric estimation of homogeneous functions

This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Consider the regression , where and the exact functional form of f is unknown, although we do know that f is homogeneous of known degree r. Using a local linear approach, we examine two ways of nonparametrically estimating f: (i) a “direct” approach and (ii) a “projection based” approach. We show that depending upon the nature of the conditional variance , one approach may be asymptotically better than the other. Results of a small simulation experiment are presented to support our findings.We thank Don Andrews and an anonymous referee for comments that greatly improved this paper. The first author thanks Professor Wolfgang Härdle for hospitality at the Institute of Statistics and Econometrics, Humboldt University, Berlin, where part of this research was carried out. Financial support to the first author from Sonderforschungsbereich 373 (“Quantifikation und Simulation Ökonomischer Prozesse”) and the NSF via grants SES-0111917 and SES-0214081 is also gratefully acknowledged.Peer Reviewe