Model Checks for Generalized Linear Models

Stute, Winfried; Zhu, Lixing

doi:10.1111/1467-9469.00304

Cited by 105 publications

(145 citation statements)

References 30 publications

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“…However, note that they …x the direction to 0 ; the direction involved in the GLM, so their approach is clearly di¤erent from that considered here, because we consider all the directions in S d simultaneously. As a consequence, our test will be consistent against all alternatives, whereas Stute and Zhu's (2002) For the family 1( 0 X u) the residual marked empirical process is given by…”

mentioning

confidence: 83%

“…Recently, Stute and Zhu (2002) have considered an innovation process transformation of R 1 n ( n ; u) for testing the correct speci…cation of GLM models, where n a suitable estimator of the GLM parameter, say 0 . More concretely, their test statistic is the CvM test…”

Section: Monte Carlo Evidencementioning

confidence: 99%

“…where B( ) a standard Brownian motion on [0; 1]; see Stute and Zhu (2002) for further details. For the nonparametric estimators we have chosen a Gaussian kernel with bandwidth h = 0:5n 1=2 ; see Stute and Zhu (2002).…”

Section: Monte Carlo Evidencementioning

confidence: 99%

“…For the nonparametric estimators we have chosen a Gaussian kernel with bandwidth h = 0:5n 1=2 ; see Stute and Zhu (2002).…”

Section: Monte Carlo Evidencementioning

confidence: 99%

“…A related approach to our is that of Stute and Zhu (2002), who considered the weighting family f1( 0 0 X u)g for model checks of GLM in a iid framework. However, note that they …x the direction to 0 ; the direction involved in the GLM, so their approach is clearly di¤erent from that considered here, because we consider all the directions in S d simultaneously.…”

mentioning

confidence: 99%

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A Consistent Diagnostic Test for Regression Models Using Projections

2006

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This paper proposes a consistent test for the goodness-of-fit of parametric regression models which overcomes two important problems of the existing tests, namely, the poor empirical power and size performance of the tests due to the curse of dimensionality and the choice of subjective parameters like bandwidths, kernels or integrating measures. We overcome these problems by using a residual marked empirical process based on projections (RMPP). We study the asymptotic null distribution of the test statistic and we show that our test is able to detect local alternatives converging to the null at the parametric rate. It turns out that the asymptotic null distribution of the test statistic depends on the data generating process, so a bootstrap procedure is considered. Our bootstrap test is robust to higher order dependence, in particular to conditional heteroskedasticity. For completeness, we propose a new minimum distance estimator constructed through the same RMPP as in the testing procedure. Therefore, the new estimator inherits all the good properties of the new test. We establish the consistency and asymptotic normality of the new minimum distance estimator. Finally, we present some Monte Carlo evidence that our testing procedure can play a valuable role in econometric regression modeling.Juan Carlos Escanciano Reyero Universidad de Navarra, Departamento de Métodos Cuantitativos Campus Universitario, 31080 Pamplona jescanci@unav.es AcknowledgmentsThe author thanks Carlos Velasco and Miguel A. Delgado for useful comments. The paper has also benefited from the comments of two referees and the Co-editor. Research funded by the Spanish Ministry of Education and Science reference number SEJ2004-04583/ECON and by the Universidad de Navarra reference number 16037001. A CONSISTENT DIAGNOSTIC TEST FOR REGRESSION MODELS USING PROJECTIONS J. Carlos EscancianoUniversidad de Navarra June 1, 2005Abstract This paper proposes a consistent test for the goodness-of-…t of parametric regression models which overcomes two important problems of the existing tests, namely, the poor empirical power and size performance of the tests due to the curse of dimensionality and the choice of subjective parameters like bandwidths, kernels or integrating measures. We overcome these problems by using a residual marked empirical process based on projections (RMPP). We study the asymptotic null distribution of the test statistic and we show that our test is able to detect local alternatives converging to the null at the parametric rate. It turns out that the asymptotic null distribution of the test statistic depends on the data generating process, so a bootstrap procedure is considered. Our bootstrap test is robust to higher order dependence, in particular to conditional heteroskedasticity. For completeness, we propose a new minimum distance estimator constructed through the same RMPP as in the testing procedure. Therefore, the new estimator inherits all the good properties of the new test. We establish the consistency and asymptotic nor...

show abstract

mentioning

confidence: 83%

Section: Monte Carlo Evidencementioning

confidence: 99%

Section: Monte Carlo Evidencementioning

confidence: 99%

“…For the nonparametric estimators we have chosen a Gaussian kernel with bandwidth h = 0:5n 1=2 ; see Stute and Zhu (2002).…”

Section: Monte Carlo Evidencementioning

confidence: 99%

mentioning

confidence: 99%

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A Consistent Diagnostic Test for Regression Models Using Projections

2006

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Nonlinear regression checking via local polynomial smoothing with applications to thermogravimetric analysis

Cao¹,

Naya²

2009

Journal of Chemometrics

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A goodness-of-fit test statistic for nonlinear regression models based on local polynomial estimation is proposed in this paper. The criterion used to construct the test is the distance between the parametric fit and the nonparametric regression estimation. The good performance of the test is shown via a simulation study. The method is applied to check a logistic mixture regression model for real data coming from a thermal analysis problem.

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A simple yet powerful test for assessing goodness‐of‐fit of high‐dimensional linear models

Zhang

Chen

et al. 2021

Statistics in Medicine

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We evaluate the validity of a projection‐based test checking linear models when the number of covariates tends to infinity, and analyze two gene expression datasets. We show that the test is still consistent and derive the asymptotic distributions under the null and alternative hypotheses. The asymptotic properties are almost the same as those when the number of covariates is fixed as long as p/n → 0 with additional mild assumptions. The test dramatically gains dimension reduction, and its numerical performance is remarkable.

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Model Checks for Generalized Linear Models

Cited by 105 publications

References 30 publications

A Consistent Diagnostic Test for Regression Models Using Projections

A Consistent Diagnostic Test for Regression Models Using Projections

Nonlinear regression checking via local polynomial smoothing with applications to thermogravimetric analysis

A simple yet powerful test for assessing goodness‐of‐fit of high‐dimensional linear models

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