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Full-Text Articles in Social and Behavioral Sciences
On Bartlett Correctability Of Empirical Likelihood In Generalized Power Divergence Family, Lorenzo Camponovo, Taisuke Otsu
On Bartlett Correctability Of Empirical Likelihood In Generalized Power Divergence Family, Lorenzo Camponovo, Taisuke Otsu
Cowles Foundation Discussion Papers
Baggerly (1998) showed that empirical likelihood is the only member in the Cressie-Read power divergence family to be Bartlett correctable. This paper strengthens Baggerly’s result by showing that in a generalized class of the power divergence family, which includes the Cressie-Read family and other nonparametric likelihood such as Schennach’s (2005, 2007) exponentially tilted empirical likelihood, empirical likelihood is still the only member to be Bartlett correctable.
Empirical Likelihood For Regression Discontinuity Design, Taisuke Otsu, Ke-Li Xu
Empirical Likelihood For Regression Discontinuity Design, Taisuke Otsu, Ke-Li Xu
Cowles Foundation Discussion Papers
This paper proposes empirical likelihood based inference methods for causal effects identified from regression discontinuity designs. We consider both the sharp and fuzzy regression discontinuity designs and treat the regression functions as nonparametric. The proposed inference procedures do not require asymptotic variance estimation and the confidence sets have natural shapes, unlike the conventional Wald-type method. These features are illustrated by simulations and an empirical example which evaluates the effect of class size on pupils’ scholastic achievements. Bandwidth selection methods, higher-order properties, and extensions to incorporate additional covariates and parametric functional forms are also discussed.
Empirical Likelihood For Nonparametric Additive Models, Taisuke Otsu
Empirical Likelihood For Nonparametric Additive Models, Taisuke Otsu
Cowles Foundation Discussion Papers
Nonparametric additive modeling is a fundamental tool for statistical data analysis which allows flexible functional forms for conditional mean or quantile functions but avoids the curse of dimensionality for fully nonparametric methods induced by high-dimensional covariates. This paper proposes empirical likelihood-based inference methods for unknown functions in three types of nonparametric additive models: (i) additive mean regression with the identity link function, (ii) generalized additive mean regression with a known non-identity link function, and (iii) additive quantile regression. The proposed empirical likelihood ratio statistics for the unknown functions are asymptotically pivotal and converge to chi-square distributions, and their associated confidence …
Moderate Deviations Of Generalized Method Of Moments And Empirical Likelihood Estimators, Taisuke Otsu
Moderate Deviations Of Generalized Method Of Moments And Empirical Likelihood Estimators, Taisuke Otsu
Cowles Foundation Discussion Papers
This paper studies moderate deviation behaviors of the generalized method of moments and generalized empirical likelihood estimators for generalized estimating equations, where the number of equations can be larger than the number of unknown parameters. We consider two cases for the data generating probability measure: the model assumption and local contaminations or deviations from the model assumption. For both cases, we characterize the first-order terms of the moderate deviation error probabilities of these estimators. Our moderate deviation analysis complements the existing literature of the local asymptotic analysis and misspecification analysis for estimating equations, and is useful to evaluate power and …
On The Asymptotic Optimality Of Empirical Likelihood For Testing Moment Restrictions, Yuichi Kitamura, Andres Santos, Azeem M. Shaikh
On The Asymptotic Optimality Of Empirical Likelihood For Testing Moment Restrictions, Yuichi Kitamura, Andres Santos, Azeem M. Shaikh
Cowles Foundation Discussion Papers
In this paper we make two contributions. First, we show by example that empirical likelihood and other commonly used tests for parametric moment restrictions, including the GMM-based J -test of Hansen (1982), are unable to control the rate at which the probability of a Type I error tends to zero. From this it follows that, for the optimality claim for empirical likelihood in Kitamura (2001) to hold, additional assumptions and qualifications need to be introduced. The example also reveals that empirical and parametric likelihood may have non-negligible differences for the types of properties we consider, even in models in which …
Testing For Non-Nested Conditional Moment Restrictions Using Unconditional Empirical Likelihood, Taisuke Otsu, Myung Hwan Seo, Yoon-Jae Whang
Testing For Non-Nested Conditional Moment Restrictions Using Unconditional Empirical Likelihood, Taisuke Otsu, Myung Hwan Seo, Yoon-Jae Whang
Cowles Foundation Discussion Papers
We propose non-nested hypotheses tests for conditional moment restriction models based on the method of generalized empirical likelihood (GEL). By utilizing the implied GEL probabilities from a sequence of unconditional moment restrictions that contains equivalent information of the conditional moment restrictions, we construct Kolmogorov-Smirnov and Cramer-von Mises type moment encompassing tests. Advantages of our tests over Otsu and Whang’s (2007) tests are: (i) they are free from smoothing parameters, (ii) they can be applied to weakly dependent data, and (iii) they allow non-smooth moment functions. We derive the null distributions, validity of a bootstrap procedure, and local and global power …
Tilted Nonparametric Estimation Of Volatility Functions With Empirical Applications, Peter C.B. Phillips, Ke-Li Xu
Tilted Nonparametric Estimation Of Volatility Functions With Empirical Applications, Peter C.B. Phillips, Ke-Li Xu
Cowles Foundation Discussion Papers
This paper proposes a novel positive nonparametric estimator of the conditional variance function without reliance on logarithmic or other transformations. The estimator is based on an empirical likelihood modification of conventional local level nonparametric regression applied to squared mean regression residuals. The estimator is shown to be asymptotically equivalent to the local linear estimator in the case of unbounded support but, unlike that estimator, is restricted to be non-negative in finite samples. It is fully adaptive to the unknown conditional mean function. Simulations are conducted to evaluate the finite sample performance of the estimator. Two empirical applications are reported. One …
Smoothed Empirical Likelihood Methods For Quantile Regression Models, Yoon-Jae Whang
Smoothed Empirical Likelihood Methods For Quantile Regression Models, Yoon-Jae Whang
Cowles Foundation Discussion Papers
This paper considers an empirical likelihood method to estimate the parameters of the quantile regression (QR) models and to construct confidence regions that are accurate in finite samples. To achieve the higher-order refinements, we smooth the estimating equations for the empirical likelihood. We show that the smoothed empirical likelihood (SEL) estimator is first-order asymptotically equivalent to the standard QR estimator and establish that confidence regions based on the smoothed empirical likelihood ratio have coverage errors of order n –1 and may be Bartlett-corrected to produce regions with an error of order n –2 , where n denotes the sample size. …