Asymptotic Comparison of Cramer-von Mises and Nonparametric Function Estimation Techniques for Testing Goodness-of-Fit

Abstract. We consider an omnibus test for the correct speci…cation of the dynamics of a sequence fx (t)g t2Z d in a lattice. As it happens with causal models and d = 1, its asymptotic distribution is not pivotal and depends on the estimator of the unknown parameters of the model under the null hypothesis. One …rst main goal of the paper is to provide a transformation to obtain an asymptotic distribution that is free of nuisance parameters. Secondly, we propose a bootstrap analogue of the transformation and show its validity. Thirdly, we discuss the results when fx (t)g t2Z d are the errors of a parametric regression model. As a by product, we also discuss the asymptotic normality of the least squares estimator of the parameters of the regression model under very mild conditions. Finally, we present a small Monte Carlo experiment to shed some light on the …nite sample behaviour of our test.JEL Classi…cation: C21, C23.

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“…On the other hand, similar arguments to those in Eubank and LaRicca (1992) imply that for a reasonable choice of q 1, tests based on…”

Section: Theorem 6 Assuming the Same Conditions Of Theorem 3 Under Hsupporting

confidence: 55%

Specification Tests for Lattice Processes

Hidalgo

Seo

2014

Econom. Theory

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“…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). In this paper we adopt the following for-25 mulation: suppose we observe…”

Section: Q5mentioning

confidence: 99%

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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“…In particular, the Cramer-von Mises (CVM) statistic has been shown to have dismal performance against almost all but location-scale alternatives. The paper by Eubank and LaRiccia (1992) presents theoretical justification for the observed phenomenon that smooth tests have superior power over CVM-type statistics for many non-location-scale alternatives. Furthermore, a natural consequence of this hazard-based formulation is our ability to obtain goodness-of-fit tests based on the model's generalized residuals, which are usually utilized for validation purposes.…”

Section: Introduction and Settingmentioning

confidence: 99%

“…In addition, both omnibus and directional tests can be generated from this class of tests. Various empirical studies such as Kopecky and Pierce (1979), Miller and Quesenberry (1979), and Eubank and LaRiccia (1992) have shown that smooth tests possess more power than commonly used omnibus test statistics for a larger class of feasible alternatives. In particular, the Cramer-von Mises (CVM) statistic has been shown to have dismal performance against almost all but location-scale alternatives.…”

Section: Introduction and Settingmentioning

confidence: 99%

A basis approach to goodness-of-fit testing in recurrent event models

Agustin

Peña

2005

Journal of Statistical Planning and Inference

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A class of tests for the hypothesis that the baseline hazard function in Cox's proportional hazards model and for a general recurrent event model belongs to a parametric family C ≡ {λ 0 (·; ξ): ξ ∈ Ξ} is proposed. Finite properties of the tests are examined via simulations, while asymptotic properties of the tests under a contiguous sequence of local alternatives are studied theoretically. An application of the tests to the general recurrent event model, which is an extended minimal repair model admitting covariates, is demonstrated. In addition, two real data sets are used to illustrate the applicability of the proposed tests.

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Asymptotic Comparison of Cramer-von Mises and Nonparametric Function Estimation Techniques for Testing Goodness-of-Fit

Cited by 88 publications

References 22 publications

Specification Tests for Lattice Processes

Specification Tests for Lattice Processes

Testing parametric assumptions of trends of a nonstationary time series

A basis approach to goodness-of-fit testing in recurrent event models

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