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89
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 182 (19 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.
Generalized Partially Linear SingleIndex Models
 Journal of the American Statistical Association
, 1998
"... The typical generalized linear model for a regression of a response Y on predictors (X; Z) has conditional mean function based upon a linear combination of (X; Z). We generalize these models to have a nonparametric component, replacing the linear combination T 0 X + T 0 Z by 0 ( T 0 X) + T 0 Z, wher ..."
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Cited by 122 (30 self)
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The typical generalized linear model for a regression of a response Y on predictors (X; Z) has conditional mean function based upon a linear combination of (X; Z). We generalize these models to have a nonparametric component, replacing the linear combination T 0 X + T 0 Z by 0 ( T 0 X) + T 0 Z, where 0 ( ) is an unknown function. We call these generalized partially linear singleindex models (GPLSIM). The models include the "singleindex" models, which have 0 = 0. Using local linear methods, estimates of the unknown parameters ( 0 ; 0 ) and the unknown function 0 ( ) are proposed, and their asymptotic distributions obtained. Examples illustrate the models and the proposed estimation methodology.
ON METHODS OF SIEVES AND PENALIZATION
, 1997
"... We develop a general theory which provides a unified treatment for the asymptotic normality and efficiency of the maximum likelihood estimates (MLE’s) in parametric, semiparametric and nonparametric models. We find that the asymptotic behavior of substitution estimates for estimating smooth function ..."
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Cited by 62 (1 self)
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We develop a general theory which provides a unified treatment for the asymptotic normality and efficiency of the maximum likelihood estimates (MLE’s) in parametric, semiparametric and nonparametric models. We find that the asymptotic behavior of substitution estimates for estimating smooth functionals are essentially governed by two indices: the degree of smoothness of the functional and the local size of the underlying parameter space. We show that when the local size of the parameter space is not very large, the substitution standard (nonsieve), substitution sieve and substitution penalized MLE’s are asymptotically efficient in the Fisher sense, under certain stochastic equicontinuity conditions of the loglikelihood. Moreover, when the convergence rate of the estimate is slow, the degree of smoothness of the functional needs to compensate for the slowness of the rate in order to achieve efficiency. When the size of the parameter space is very large, the standard and penalized maximum likelihood procedures may be inefficient, whereas the method of sieves may be able to overcome this difficulty. This phenomenon is particularly manifested when the functional of interest is very smooth, especially in the semiparametric case.
Semiparametric Analysis of German EastWest Migration Intentions: Facts and Theory
 JOURNAL OF APPLIED ECONOMETRICS
, 1997
"... EastWest migration in Germany peaked at the beginning of the 90s although the average wage gap between Eastern and Western Germany continues to average about 25%. We analyze the propensity to migrate using microdata from the German Socioeconomic Panel. Fitting a parametric Generalized Linear Model ..."
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Cited by 62 (1 self)
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EastWest migration in Germany peaked at the beginning of the 90s although the average wage gap between Eastern and Western Germany continues to average about 25%. We analyze the propensity to migrate using microdata from the German Socioeconomic Panel. Fitting a parametric Generalized Linear Model (GLM) yields nonlinear residual behavior. This finding is not compatible with classical Marshallian theory of migration and motivates the semiparametric analysis. We estimate a Generalized Partial Linear Model (GPLM) where some components of the index of explanatory variables enter nonparametrically. We find the estimate of the nonparametric influence in concordance with a number of alternative migration theories, including the recently proposed optionvalueofwaiting theory.
Semiparametric Regression For Clustered Data Using Generalized Estimating Equations
 Journal of the American Statistical Association
, 2001
"... We consider estimation in a semiparametric generalized linear model for clustered data using estimating equations. Our results apply to the case that the number of observations per cluster is finite, while the number of clusters is large. The mean of the outcome variable is of the form g( ) = X T + ..."
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Cited by 55 (12 self)
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We consider estimation in a semiparametric generalized linear model for clustered data using estimating equations. Our results apply to the case that the number of observations per cluster is finite, while the number of clusters is large. The mean of the outcome variable is of the form g( ) = X T + (T ), where g( ) is a link function, X and T are covariates, is an unknown parameter vector and (t) is an unknown smooth function. Kernel estimating equations proposed previously in the literature are used to estimate the infinite dimensional nonparametric function (t) and a profilebased estimating equation is used to estimate the nite dimensional parameter vector . We show that for clustered data this conventional profile/kernel method often fails to yield a p n consistent estimator of along with appropriate inference unless working independence is assumed or (t) is artificially undersmoothed, in which case asymptotic inference is possible. To gain insight of these results, we derive the semiparametric efficient score of , which is found to have a complicated form, and show that unlike for independent data, the profile/kernel method does not yield a score function asymptotically equivalent to the semiparametric efficient score of , even when the true correlation is assumed and (t) is undersmoothed. We illustrate the methods with an application to infectious disease data and evaluate their finite sample performance through a simulation study.
2007): “Understanding Bias in Nonlinear Panel Models: Some Recent Developments
 Advances in Economics and Econometrics, Ninth World Congress
"... The purpose of this paper is to review recently developed biasadjusted methods of estimation of nonlinear panel data models with fixed effects. For some models, like static linear and logit regressions, there exist fixedT consistent estimators as n →∞. Fixed T consistency is a desirable property b ..."
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Cited by 50 (7 self)
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The purpose of this paper is to review recently developed biasadjusted methods of estimation of nonlinear panel data models with fixed effects. For some models, like static linear and logit regressions, there exist fixedT consistent estimators as n →∞. Fixed T consistency is a desirable property because for many panels T is much smaller than n.
An Adaptive Estimation of Dimension Reduction Space
, 2002
"... Searching for an effective dimension reduction space is an important problem in regression, especially for high dimensional data. In this paper, we propose an adaptive approach based on semiparametric models, which we call the minimum average (conditional) variance estimation (MAVE) method, within q ..."
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Cited by 46 (2 self)
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Searching for an effective dimension reduction space is an important problem in regression, especially for high dimensional data. In this paper, we propose an adaptive approach based on semiparametric models, which we call the minimum average (conditional) variance estimation (MAVE) method, within quite a general setting. The MAVE method has the following advantages: (1) Most existing methods have to undersmooth the nonparametric link function estimator in order to achieve a faster rate of consistency for the estimator of the parameters (than for that of the nonparametric function). In contrast, a faster consistency rate can be achieved by the MAVE method even without undersmoothing the nonparametric link function estimator. (2) The MAVE method is applicable to a wide range of models, with fewer restrictions on the distribution of the covariates, to the extent that even time series can be included. (3) Because of the faster rate of consistency for the parameter estimators, it is possible for us to estimate the dimension of the space consistently.
Estimating semiparametric ARCH(∞) models by kernel smoothing methods
 Econometrica
, 2005
"... Contents: ..."
Penalized maximum likelihood and semiparametric secondorder efficiency
 ANN. STATIST
, 2006
"... We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric secondorder efficiency and propose estimators that are semiparametrically efficient and secondorder efficient in our model. These estimators ..."
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Cited by 30 (5 self)
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We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric secondorder efficiency and propose estimators that are semiparametrically efficient and secondorder efficient in our model. These estimators are of a penalized maximum likelihood type with an appropriately chosen penalty. We argue that secondorder efficiency is crucial in semiparametric problems since only the secondorder terms in asymptotic expansion for the risk account for the behavior of the “nonparametric component” of a semiparametric procedure, and they are not dramatically smaller than the firstorder terms.