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31
Splinebackfitted kernel smoothing of nonlinear additive autoregression model
, 2007
"... Application of nonparametric and semiparametric regression techniques to highdimensional time series data has been hampered due to the lack of effective tools to address the “curse of dimensionality.” Under rather weak conditions, we propose splinebackfitted kernel estimators of the component func ..."
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Cited by 25 (14 self)
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Application of nonparametric and semiparametric regression techniques to highdimensional time series data has been hampered due to the lack of effective tools to address the “curse of dimensionality.” Under rather weak conditions, we propose splinebackfitted kernel estimators of the component functions for the nonlinear additive time series data that are both computationally expedient so they are usable for analyzing very highdimensional time series, and theoretically reliable so inference can be made on the component functions with confidence. Simulation experiments have provided strong evidence that corroborates the asymptotic theory.
Nonparametric estimation and testing of fixed effects panel data models
 Journal of Econometrics
, 2008
"... In this paper we consider the problem of estimating nonparametric panel data models with fixed effects. We derive the rate of convergence and asymptotic distribution of an iterative nonparametric kernel estimator. We also extend the estimation method to the case of a semiparametric partially linear ..."
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Cited by 25 (3 self)
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In this paper we consider the problem of estimating nonparametric panel data models with fixed effects. We derive the rate of convergence and asymptotic distribution of an iterative nonparametric kernel estimator. We also extend the estimation method to the case of a semiparametric partially linear fixed effects model. To determine whether a parametric, semiparametric or nonparametric model is appropriate, we propose test statistics to test between the three alternatives in practice. We further propose a test statistic for testing the null hypothesis of random effects against fixed effects in a nonparametric panel data regression model. Simulations are used to examine the finite sample performance of the proposed estimators and the test statistics.
Additive isotone regression
 In: Asymptotics: Particles, Processes and Inverse Problems: Festschrift for Piet Groeneboom. IMS
, 2007
"... This paper is dedicated to Piet Groeneboom on the occasion of his 65th birthday Abstract: This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymptotically up to first order, each additive component can be estimat ..."
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Cited by 11 (0 self)
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This paper is dedicated to Piet Groeneboom on the occasion of his 65th birthday Abstract: This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymptotically up to first order, each additive component can be estimated as well as it could be by a least squares estimator if the other components were known. The algorithm for the calculation of the estimator uses backfitting. Convergence of the algorithm is shown. Finite sample properties are also compared through simulation experiments. 1.
Additive regression splines with irrelevant categorical and continuous regressors. Statistica Sinica
, 2013
"... Abstract: We consider the problem of estimating a relationship using semiparametric additive regression splines when there exist both continuous and categorical regressors, some of which are irrelevant but this is not known a priori. We show that choosing the spline degree, number of subintervals, ..."
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Cited by 5 (1 self)
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Abstract: We consider the problem of estimating a relationship using semiparametric additive regression splines when there exist both continuous and categorical regressors, some of which are irrelevant but this is not known a priori. We show that choosing the spline degree, number of subintervals, and bandwidths via crossvalidation can automatically remove irrelevant regressors, thereby delivering 'automatic dimension reduction' without the need for pretesting. Theoretical underpinnings are provided, finitesample performance is studied, and an illustrative application demonstrates the efficacy of the proposed approach in finitesample settings. An R package implementing the methods is available from the Comprehensive R Archive Network (Racine and Nie
Estimation in Additive Models with Highly or Nonhighly Correlated Covariates,”The Annals of Statistics
, 2010
"... Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive components, integration estimation and pooled backfitting estimat ..."
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Cited by 4 (0 self)
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Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive components, integration estimation and pooled backfitting estimation. The former is designed for highly correlated covariates, and the latter is useful for nonhighly correlated covariates. Asymptotic normalities of the proposed estimators are established. Simulations are conducted to demonstrate finite sample behaviors of the proposed estimators, and real data examples are given to illustrate the value of the methodology. 1. Introduction. The
Efficient semiparametric regression for longitudinal data with nonparametric covariance estimation
, 2011
"... ..."
A Loss Function Approach to Model Specification Testing and Its Relative Efficiency to the GLR Test
, 2009
"... The generalized likelihood ratio (GLR) test is proposed by Fan, Zhang and Zhang (2001) as a generally applicable statistical method to test parametric, semiparametric or nonparametric models against nonparametric alternative models. It is a natural extension of the maximum likelihood ratio test for ..."
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Cited by 2 (0 self)
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The generalized likelihood ratio (GLR) test is proposed by Fan, Zhang and Zhang (2001) as a generally applicable statistical method to test parametric, semiparametric or nonparametric models against nonparametric alternative models. It is a natural extension of the maximum likelihood ratio test for parametric models and fully inherits the advantages of the classical likelihood ratio test. Both true likelihood and pseudo likelihood functions can be used. Like the classical likelihood ratio test, the GLR test enjoys the appealing Wilks phenomena in the sense that its asymptotic distribution is free of nuisance parameters and nuisance functions, and follows a χ2distribution with a known large number of degrees of freedom. It achieves the asymptotically optimal rate of convergence for nonparametric testing problems formulated by Ingster (1993a, 1993b) and Spokoiny (1996). In this paper, we propose a class of new tests based on loss functions, which measure the discrepancies between the fitted values of the null and nonparametric alternative models, and are often more relevant to applications. Like the GLR test, the loss functionbased test is generally applicable and enjoy many appealing features of the GLR test, including the Wilks phenomena. Most importantly,
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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Cited by 2 (2 self)
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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.
a) Nonparametric Model Checking and Variable Selection
, 2012
"... Let X be a d dimensional vector of covariates and Y be the response variable. Under the nonparametric model Y = m(X) + σ(X) we develop an ANOVAtype test for the null hypothesis that a particular coordinate of X has no influence on the regression function. The asymptotic distribution of the test st ..."
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Cited by 1 (0 self)
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Let X be a d dimensional vector of covariates and Y be the response variable. Under the nonparametric model Y = m(X) + σ(X) we develop an ANOVAtype test for the null hypothesis that a particular coordinate of X has no influence on the regression function. The asymptotic distribution of the test statistic, using residuals based on NadarayaWatson type kernel estimator and d ≤ 4, is established under the null hypothesis and local alternatives. Simulations suggest that under a sparse model, the applicability of the test extends to arbitrary d through sufficient dimension reduction. Using pvalues from this test, a variable selection method based on multiple testing ideas is proposed. The proposed test outperforms existing procedures, while additional simulations reveal that the proposed variable selection method performs competitively against well established procedures. A real data set is analyzed.
Testing for Constant Nonparametric Effects in General Semiparametric Regression Models with Interactions
"... We consider the problem of testing for a constant nonparametric effect in a general semiparametric regression model when there is the potential for interaction between the parametrically and nonparametrically modeled variables. The work was originally motivated by a unique testing problem in genetic ..."
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We consider the problem of testing for a constant nonparametric effect in a general semiparametric regression model when there is the potential for interaction between the parametrically and nonparametrically modeled variables. The work was originally motivated by a unique testing problem in genetic epidemiology (Chatterjee, et al., 2006) that involved a typical generalized linear model but with an additional term reminiscent of the Tukey onedegreeoffreedom formulation, and their interest was in testing for main effects of the genetic variables, while gaining statistical power by allowing for a possible interaction between genes and the environment. Later work (Maity, et al., 2009) involved the possibility of modeling the environmental variable nonparametrically, but they focused on whether there was a parametric main effect for the genetic variables. In this paper, we consider the complementary problem, where the interest is in testing for the main effect of the nonparametrically modeled environmental variable. We derive a generalized likelihood ratio test for this hypothesis, show how to implement it, and provide evidence that our method can improve statistical power when compared to standard partially linear models with main effects only. We also demonstrate our method by analyzing data from a casecontrol study of colorectal adenoma.