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Large Sample Sieve Estimation of SemiNonparametric Models
 Handbook of Econometrics
, 2007
"... Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; seminonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method o ..."
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Cited by 92 (17 self)
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Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; seminonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method of sieves provides one way to tackle such complexities by optimizing an empirical criterion function over a sequence of approximating parameter spaces, called sieves, which are significantly less complex than the original parameter space. With different choices of criteria and sieves, the method of sieves is very flexible in estimating complicated econometric models. For example, it can simultaneously estimate the parametric and nonparametric components in seminonparametric models with or without constraints. It can easily incorporate prior information, often derived from economic theory, such as monotonicity, convexity, additivity, multiplicity, exclusion and nonnegativity. This chapter describes estimation of seminonparametric econometric models via the method of sieves. We present some general results on the large sample properties of the sieve estimates, including consistency of the sieve extremum estimates, convergence rates of the sieve Mestimates, pointwise normality of series estimates of regression functions, rootn asymptotic normality and efficiency of sieve estimates of smooth functionals of infinite dimensional parameters. Examples are used to illustrate the general results.
Penalized Sieve Estimation and Inference of Seminonparametric Dynamic Models: A Selective Review
, 2011
"... In this selective review, we …rst provide some empirical examples that motivate the usefulness of seminonparametric techniques in modelling economic and …nancial time series. We describe popular classes of seminonparametric dynamic models and some temporal dependence properties. We then present pe ..."
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Cited by 3 (1 self)
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In this selective review, we …rst provide some empirical examples that motivate the usefulness of seminonparametric techniques in modelling economic and …nancial time series. We describe popular classes of seminonparametric dynamic models and some temporal dependence properties. We then present penalized sieve extremum (PSE) estimation as a general method for seminonparametric models with crosssectional, panel, time series, or spatial data. The method is especially powerful in estimating di ¢ cult illposed inverse problems such as seminonparametric mixtures or conditional moment restrictions. We review recent advances on inference and large sample properties of the PSE estimators, which include (1) consistency and convergence rates of the PSE estimator of the nonparametric part; (2) limiting distributions of plugin PSE estimators of functionals that are either smooth (i.e., rootn estimable) or nonsmooth (i.e., slower than rootn estimable); (3) simple criterionbased inference for plugin PSE estimation of smooth or nonsmooth functionals; and (4) rootn asymptotic normality of semiparametric twostep estimators and their consistent variance estimators. Examples from dynamic asset pricing, nonlinear spatial VAR, semiparametric GARCH,