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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 185 (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.
Endogeneity in Nonparametric and Semiparametric Regression Models
, 2000
"... This paper considers the nonparametric and semiparametric methods for estimating regression models with continuous endogenous regressors. We list a number of different generalizations of the linear structural equation model, and discuss how three common estimation approaches for linear equations — t ..."
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Cited by 130 (19 self)
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This paper considers the nonparametric and semiparametric methods for estimating regression models with continuous endogenous regressors. We list a number of different generalizations of the linear structural equation model, and discuss how three common estimation approaches for linear equations — the “instrumental variables, ” “fitted value, ” and “control function ” approaches — may or may not be applicable to nonparametric generalizations of the linear model and to their semiparametric variants. The discussion then turns to a particular semiparametric model, the binary response model with linear index function and nonparametric error distribution, and describes in detail how estimation of the parameters of interest can be constructed using the “control function ” approach. This estimator is then applied to an empirical problem of the relation of labor force participation to nonlabor income, viewed as an endogenous regressor.
Instrumental variable treatment of nonclassical measurement error models.
 Econometrica,
, 2008
"... Abstract While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary dataset containing correctly measured observations, we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors ..."
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Cited by 64 (18 self)
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Abstract While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary dataset containing correctly measured observations, we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errorsinvariables models with continuously distributed variables. Our main identifying assumption is that, conditional on the value of the true regressors, some "measure of location" of the distribution of the measurement error (e.g. its mean, mode or median) is equal to zero. The proposed approach relies on the eigenvalueeigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to "index" the eigenfunctions so that the decomposition is unique. We propose a convenient sievebased estimator, derive its asymptotic properties and investigate its finitesample behavior through Monte Carlo simulations.
Monte Carlo algorithms for optimal stopping and statistical learning
, 2003
"... We extend the LongstaffSchwartz algorithm for approximately solving optimal stopping problems on highdimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical learning problem. Within this setup we apply deviation ineq ..."
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Cited by 34 (2 self)
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We extend the LongstaffSchwartz algorithm for approximately solving optimal stopping problems on highdimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical learning problem. Within this setup we apply deviation inequalities for suprema of empirical processes to derive consistency criteria, and to estimate the convergence rate and sample complexity. Our results strengthen and extend earlier results obtained by Clément, Lamberton and Protter (2002).
Inverse Problems as Statistics
 INVERSE PROBLEMS
, 2002
"... What mathematicians, scientists, engineers, and statisticians mean by "inverse problem" differs. For a statistician, an inverse problem is an inference or estimation problem... ..."
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Cited by 21 (3 self)
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What mathematicians, scientists, engineers, and statisticians mean by "inverse problem" differs. For a statistician, an inverse problem is an inference or estimation problem...
Semiparametric efficiency in GMM models with auxiliary data
 Ann. Statist
, 2008
"... We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are obser ..."
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Cited by 20 (3 self)
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We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database, when such distribution is common to the two data sets. The auxiliary sample can be independent of the primary sample, or can be a subset of it. For both cases, we derive bounds when the probability of missing data given the proxy variables is unknown, or known, or belongs to a correctly specified parametric family. We find that the conditional probability is not ancillary when the two samples are independent. For all cases, we discuss efficient semiparametric estimators. An estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting. 1. Introduction. Many
Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos
, 2000
"... This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the est ..."
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Cited by 19 (3 self)
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This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the estimated Lyapunov exponents and a consistent variance estimator. A simulation study to evaluate small sample performance is reported. We also apply our procedures to daily stock return data. In most cases, the hypothesis of chaos in the stock return series is rejected at the 1 % level with an exception in some higher power transformed absolute returns.
Estimation of the Binary Response Model using a Mixture of Distributions Estimator (MOD)
, 2000
"... This paper develops a semiparametric sieve estimator, which is termed a mixture of distributions estimator (MOD), to estimate a binary response model when the distribution of the errors is unknown. The estimator for the distribution function is composed of a mixture of smooth distributions, where th ..."
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Cited by 10 (0 self)
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This paper develops a semiparametric sieve estimator, which is termed a mixture of distributions estimator (MOD), to estimate a binary response model when the distribution of the errors is unknown. The estimator for the distribution function is composed of a mixture of smooth distributions, where the number of mixtures increases with the sample size. The model is semiparametric because it is assumed that a parametric index type restriction holds. Optimal rates of convergence are established for the distribution function under the L_2 norm, and conditions are derived under which estimates of the parametric component are asymptotically normal. An appealing feature about MOD is that it is possible to restrict the estimator of the distribution function, a priori, to be smooth, nonnegative, increasing, and to integrate to one. This has important practical and theoretical implications.
2011): “Nonlinear Panel Data Analysis
 Annual Review of Economics
"... Nonlinear panel data models arise naturally in economic applications, yet their analysis is challenging. Here we provide a progress report on some recent advances in the area. We start by reviewing the properties of randomeffects likelihood approaches. We emphasize a link with Bayesian computation ..."
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Cited by 9 (0 self)
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Nonlinear panel data models arise naturally in economic applications, yet their analysis is challenging. Here we provide a progress report on some recent advances in the area. We start by reviewing the properties of randomeffects likelihood approaches. We emphasize a link with Bayesian computation and Markov Chain Monte Carlo, which provides a convenient approach to estimation and inference. Relaxing parametric assumptions on the distribution of individual effects raises serious identification problems. In discrete choice models, common parameters and average marginal effects are generally setidentified. The availability of continuous outcomes, however, provides opportunities for pointidentification. We end the paper by reviewing recent progress on non fixedT approaches. In panel applications where the time dimension is not negligible relative to the size of the crosssection, it makes sense to view the estimation problem as a timeseries finite sample bias. Several perspectives to bias reduction are now available. We review their properties, with a special emphasis on randomeffects methods. JEL codes: C23.