Comparing Nonparametric Versus Parametric Regression Fits

Härdle, Wolfgang Karl; Mammen, Enno

doi:10.1214/aos/1176349403

Cited by 1,004 publications

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“…1, which shows that the normal Q3 approximation does not have a satisfactory finite-sample performance. A similar phenomenon was observed by Härdle & Mammen (1993). If we ignore the inherited dependence structure, then one may obtain an erroneous conclusion; see Fig.…”

supporting

confidence: 71%

“…Parametric models have the advantage of ease of interpretation and prediction, but 20 may suffer from misspecification, leading to erroneous conclusions. Hypothesis testing in nonparametric regression under independence has been discussed by Härdle & Mammen (1993), Hart (1997), Fan et al (2001) and Van Keilegom et al (2008). Other contributions can be found in Azzalini et al (1989), Eubank & LaRiccia (1992), Aerts et al (1999), Eubank (1999), Horowitz & Spokoiny (2001) and Fan & Jiang (2007).…”

Section: Q5mentioning

confidence: 99%

“…Such a bias correction scheme was previously used in Härdle & Mammen (1993). Note that ISE M is not directly usable since it depends on the unknown function μ, which under H 0 depends on the parameter θ 0 .…”

mentioning

confidence: 99%

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Testing parametric assumptions of trends of a nonstationary time series

Zhang

2011

Biometrika

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SUMMARYThe paper considers testing whether the mean trend of a nonstationary time series is of certain parametric forms. A central limit theorem for the integrated squared error is derived, and with that a hypothesis-testing procedure is proposed. The method is illustrated in a simulation study, and is applied to assess the mean pattern of lifetime-maximum wind speeds of global tropical cyclones from 1981 to 2006. We also revisit the trend pattern in the central England temperature series.

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confidence: 71%

Section: Q5mentioning

confidence: 99%

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Testing parametric assumptions of trends of a nonstationary time series

Zhang

2011

Biometrika

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“…The statistic T n is a modification of the test statistic discussed by Härdle and Mammen (1993) for the random sample case. The test was used in Gao, Tjøstheim, and Yin (2012) for a nonlinear cointegrating model with a martingale error structure and no endogeneity.…”

Section: Model Specification Testingmentioning

confidence: 99%

Nonparametric Cointegrating Regression With Endogeneity and Long Memory

Wang¹,

Phillips

2014

Econom. Theory

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This paper explores nonparametric estimation, inference, and specification testing in a nonlinear cointegrating regression model where the structural equation errors are serially dependent and where the regressor is endogenous and may be driven by long memory innovations. Generalizing earlier results of Wang and Phillips (2009a,b, Econometric Theory 25, 710-738, Econometrica 77, 1901-1948), the conventional nonparametric local level kernel estimator is shown to be consistent and asymptotically (mixed) normal in these cases, thereby opening up inference by conventional nonparametric methods to a wide class of potentially nonlinear cointegrated relations. New results on the consistency of parametric estimates in nonlinear cointegrating regressions are provided, extending earlier research on parametric nonlinear regression and providing primitive conditions for parametric model testing. A model specification test is studied and confirmed to provide a valid mechanism for testing parametric specifications that is robust to endogeneity. But under long memory innovations the test is not pivotal, its convergence rate is parameter dependent, and its limit theory involves the local time of fractional Brownian motion. Simulation results show good performance for the nonparametric kernel estimates in cases of strong endogeneity and long memory, whereas the specification test is shown to be sensitive to the presence of long memory innovations, as predicted by asymptotic theory.

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“…The asymptotic distribution of the test statistic (2.3) can be obtained using arguments as in Ait-Sahalia, Bickel and Stoker (2002), and because the large sample behavior of this test is not in the center of the paper we desist from presenting it here. Arguments for the consistency of bootstrap based procedures for the asymptotic distribution may be found there, as well as in Härdle and Mammen (1993). The following bootstrap procedure seems natural:…”

Section: Testing Conditional Normalitymentioning

confidence: 99%

Demand Analysis as an Ill-Posed Inverse Problem With Semiparametric Specification

Hoderlein

Holzmann²

2010

Econom. Theory

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In this paper we are concerned with analyzing the behavior of a semiparametric estimator which corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly normal, conditional on exogenous regressors. This leads to a severely ill-posed inverse problem. In this setup, we show first how to test for conditional normality. More importantly, we then establish how to exploit this knowledge when constructing an estimator, and we derive results characterizing the large sample behavior of such an estimator.In addition, in a Monte Carlo experiment we analyze the finite sample behavior of the proposed estimator.Our application comes from consumer demand. We obtain new and interesting findings that highlight both the advantages, and the difficulties of an approach which leads to ill-posed inverse problems. Finally, we discuss the somewhat problematic relationship between nonparametric instrumental variable models, and the recently emphasized issue of unobserved heterogeneity in structural models.

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Comparing Nonparametric Versus Parametric Regression Fits

Cited by 1,004 publications

References 0 publications

Testing parametric assumptions of trends of a nonstationary time series

Testing parametric assumptions of trends of a nonstationary time series

Nonparametric Cointegrating Regression With Endogeneity and Long Memory

Demand Analysis as an Ill-Posed Inverse Problem With Semiparametric Specification

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