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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 89 (13 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.
2007a) Testing the suitability of polynomial models in errorsinvariables problems
 Ann. Statist
"... A lowdegree polynomial model for a response curve is used commonly in practice. It generally incorporates a linear or quadratic function of the covariate. In this paper we suggest methods for testing the goodness of fit of a general polynomial model when there are errors in the covariates. There, t ..."
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Cited by 2 (2 self)
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A lowdegree polynomial model for a response curve is used commonly in practice. It generally incorporates a linear or quadratic function of the covariate. In this paper we suggest methods for testing the goodness of fit of a general polynomial model when there are errors in the covariates. There, the true covariates are not directly observed, and conventional bootstrap methods for testing are not applicable. We develop a new approach, in which deconvolution methods are used to estimate the distribution of the covariates under the null hypothesis, and a “wild ” or momentmatching bootstrap argument is employed to estimate the distribution of the experimental errors (distinct from the distribution of the errors in covariates). Most of our attention is directed at the case where the distribution of the errors in covariates is known, although we also discuss methods for estimation and testing when the covariate error distribution is estimated. No assumptions are made about the distribution of experimental error, and, in particular, we depart substantially from conventional parametric models for errorsinvariables problems.
Nonparametric estimation of meansquared prediction error in nestederror regression models. Available at http://arxiv.org/abs/math/0509493
, 2005
"... Nestederror regression models are widely used for analyzing clustered data. For example, they are often applied to twostage sample surveys, and in biology and econometrics. Prediction is usually the main goal of such analyses, and meansquared prediction error is the main way in which prediction p ..."
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Cited by 2 (1 self)
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Nestederror regression models are widely used for analyzing clustered data. For example, they are often applied to twostage sample surveys, and in biology and econometrics. Prediction is usually the main goal of such analyses, and meansquared prediction error is the main way in which prediction performance is measured. In this paper we suggest a new approach to estimating meansquared prediction error. We introduce a matchedmoment, doublebootstrap algorithm, enabling the notorious underestimation of the naive meansquared error estimator to be substantially reduced. Our approach does not require specific assumptions about the distributions of errors. Additionally, it is simple and easy to apply. This is achieved through using Monte Carlo simulation to implicitly develop formulae which, in a more conventional approach, would be derived laboriously by mathematical arguments. 1. Introduction. Unbalanced
with Cross Section Dependence ∗
, 2010
"... In this paper we propose a nonparametric test for poolability in large dimensional semiparametric panel data models with crosssection dependence based on the sieve estimation technique. To construct the test statistic, we only need to estimate the model under the alternative. We establish the asymp ..."
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In this paper we propose a nonparametric test for poolability in large dimensional semiparametric panel data models with crosssection dependence based on the sieve estimation technique. To construct the test statistic, we only need to estimate the model under the alternative. We establish the asymptotic normal distributions of our test statistic under the null hypothesis of poolability and a sequence of local alternatives, and prove the consistency of our test. We also suggest a bootstrap method as an alternative way to obtain the critical values and justify its validity. A small set of Monte Carlo simulations indicate the test performs reasonably well in finite samples.
Local Instrumental Variable (LIVE) Method For The Generalized AdditiveInteractive Nonlinear Volatility Model
"... In this article we consider a new separable nonparametric volatility model that includes secondorder interaction terms in both mean and conditional variance functions. This is a very flexible nonparametric ARCH model that can potentially explain the behavior of the wide variety of financial assets ..."
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In this article we consider a new separable nonparametric volatility model that includes secondorder interaction terms in both mean and conditional variance functions. This is a very flexible nonparametric ARCH model that can potentially explain the behavior of the wide variety of financial assets. The model is estimated using the generalized version of the Local Instrumental Variable Estimation method (LIVE) first introduced in Kim and Linton (2004). This method is computationally more effective than most other nonparametric estimation methods that can potentially be used to estimate components of such a model. Asymptotic behavior of the resulting estimators is investigated and their asymptotic normality is established. Explicit expressions for asymptotic means and variances of these estimators are also obtained.
OPTIMAL TESTING FOR ADDITIVITY IN MULTIPLE NONPARAMETRIC REGRESSION Short title: Testing Additivity
"... We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) nonadaptive and adaptive hypothesis testing procedures for additivity against the composite nonparametric alternative that the response function involv ..."
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We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) nonadaptive and adaptive hypothesis testing procedures for additivity against the composite nonparametric alternative that the response function involves interactions of second or higher orders separated away from zero in L 2 ([0,1] d)norm and also possesses some smoothness properties. In order to shed some light on the theoretical results obtained, we carry out a wide simulation study to examine the finite sample performance of the proposed hypothesis testing procedures and compare them with a series of other tests for additivity available in the literature.
Consistent Model Specification Tests Against Smooth Transition Alternatives ∗
, 2005
"... In this paper we develop tests of functional form that are consistent against a class of nonlinear "smooth transition " models of the conditional mean. Our method is an extension of the consistent model specification tests developed by Bierens (1990), de Jong (1996) and Bierens and Ploberg ..."
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In this paper we develop tests of functional form that are consistent against a class of nonlinear "smooth transition " models of the conditional mean. Our method is an extension of the consistent model specification tests developed by Bierens (1990), de Jong (1996) and Bierens and Ploberger (1997), provides maximal power against nonlinear smooth transition ARX specifications, and is consistent against any deviation from the null hypothesis. Of separate interest, we provide substantial detail regarding when and whether Bierenstype tests are asymptotically degenerate. In a simulation experiment in which all parameters are randomly selected, and a linear AR null model is selected by minimizing the AIC, the proposed test has power nearly identical to a most powerful test for true STAR processes, and dominates popular tests. 1. Introduction Smooth Transition Threshold Autoregressive (STAR)