Testing Structural Change in Partially Linear Models

Su, Liangjun; White, Halbert

doi:10.1017/s0266466609990788

Cited by 23 publications

(10 citation statements)

References 38 publications

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“…Previous work on testing conditional independence for continuous random variables includes Linton and Gozalo (1997, "LG"), Fernandes and Flores (1999, "FF"), and Delgado and Gonzalez-Manteiga (2001, "DG"). Su and White have several papers ( , 2008( , 2010 addressing this question. Although SW's tests are consistent against any deviation from the null, they are only able to detect local alternatives converging to the null at a rate slower than n −1/2 and hence suffer from the "curse of dimensionality."…”

Section: Introductionmentioning

confidence: 99%

A Flexible Nonparametric Test for Conditional Independence

2015

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This paper proposes a nonparametric test for conditional independence that is easy to implement, yet powerful in the sense that it is consistent and achieves n −1/2 local power. The test statistic is based on an estimator of the topological "distance" between restricted and unrestricted probability measures corresponding to conditional independence or its absence. The distance is evaluated using a family of Generically Comprehensively Revealing (GCR) functions, such as the exponential or logistic functions, which are indexed by nuisance parameters. The use of GCR functions makes the test able to detect any deviation from the null. We use a kernel smoothing method when estimating the distance. An integrated conditional moment (ICM) test statistic based on these estimates is obtained by integrating out the nuisance parameters. We simulate the critical values using a conditional simulation approach. Monte Carlo experiments show that the test performs well in finite samples. As an application, we test an implication of the key assumption of unconfoundedness in the context of estimating the returns to schooling.

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Section: Introductionmentioning

confidence: 99%

A Flexible Nonparametric Test for Conditional Independence

2015

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“…Examples are the weighted likelihood ratio test in Picard (1985) and Andrews and Ploberger (1994); Wald and Lagrange multiplier tests in Hansen (1992), Andrews (1993), and Bai and Perron (1998); the exact likelihood ratio test in Horváth (1993) and Davis, Huang, and Yao (1995); the empirical approach in Bai (1996) for regression models; and the sequential test in Lai (1995). Su and White (2010) proposed two tests for change-points in partially linear models. Breitung This paper develops an asymptotic theory for estimating change-points in linear and nonlinear time series models.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Change-Points in Linear and Nonlinear Time Series Models

Ling

2014

Econom. Theory

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This paper develops an asymptotic theory for estimated change-points in linear and nonlinear time series models. Based on a measurable objective function, it is shown that the estimated change-point converges weakly to the location of the maxima of a double-sided random walk and other estimated parameters are asymptotically normal. When the magnitude d of changed parameters is small, it is shown that the limiting distribution can be approximated by the known distribution as in Yao (1987, Annals of Statistics 15, 1321-1328. This provides a channel to connect our results with those in Picard (1985, Advances in Applied Probability 17, 841-867) and Bai, Lumsdaine, and Stock (1998, Review of Economic Studies 65, 395-432), where the magnitude of changed parameters depends on the sample size n and tends to zero as n → ∞. The theory is applied for the self-weighted QMLE and the local QMLE of change-points in ARMA-GARCH/IGARCH models. A simulation study is carried out to evaluate the performance of these estimators in the finite sample. 1 2 SHIQING LING and Eickmeier (2011) and Han and Inoue (2014) studied some tests for structural breaks in dynamic factor models. Ling (2007a) developed an asymptotic theory of the Quandt-type tests for linear and nonlinear time series models. Aue, Hörmann, Horváth, and Reimherr (2009) studied the break detection in the covariance structure of multivariate time series models. Shao and Zhang (2010) studied Quandt-type test for the change of mean in time series. This type of tests was further developed by Hidalgo and Seo (2013) under a larger framework. Empirically, we want to know not only that structural change exists, but also the location of change-point.The first paper on the estimation of change-points is by Hinkley (1970), in which he investigated the maximum likelihood estimator (MLE) of the change-points in a sequence of i.i.d. random variables and proved that the estimated change-point converges in distribution to the location of the maxima of a double-sided random walk. Under the normality assumption, he showed that the limiting distribution can be tabulated by a numerical method. Hinkley and Hinkley (1970) used a similar method to investigate the binomial random variables and showed that the limiting distribution has a computable form. However, for the nonnormal or nonbinomial cases, their results cannot be used as statistical inference for the change point. When the magnitude d of changed parameters is small, Yao (1987) showed that Hinkley's (1970) limiting distribution can be approximated by a very nice distribution. Ritov (1990) studied the asymptotic efficient estimation of the change-point. Dümbgen (1991) investigated the nonparametric method for change-point estimators. Bai (1995) studied a structure-changed regression model with a fixed d and showed that the estimated change-point converges in distribution to the location of the maxima of a double-sided random walk. Qu and Perron (2007) investigated estimating and testing structural changes in multivariate regressions. H...

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“…They allow for nonstationarities in the covariates but analyze the behavior of their test statistic only on a rather specific type of (local) alternatives. Finally, Su and White (2010) set up a test for structural change in partially linear models.…”

Section: Introductionmentioning

confidence: 99%

Testing for Structural Change in Time-Varying Nonparametric Regression Models

Vogt

2014

Econom. Theory

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In this paper, we consider a nonparametric model with a time-varying regression function and locally stationary regressors. We are interested in the question whether the regression function has the same shape over a given time span. To tackle this testing problem, we propose a kernel-based L 2 -test statistic. We derive the asymptotic distribution of the statistic both under the null and under fixed and local alternatives. To improve the small sample behavior of the test, we set up a wild bootstrap procedure and derive the asymptotic properties thereof. The theoretical analysis of the paper is complemented by a simulation study and a real data example.

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Testing Structural Change in Partially Linear Models

Cited by 23 publications

References 38 publications

A Flexible Nonparametric Test for Conditional Independence

A Flexible Nonparametric Test for Conditional Independence

Estimation of Change-Points in Linear and Nonlinear Time Series Models

Testing for Structural Change in Time-Varying Nonparametric Regression Models

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