Testing Parametric versus Semiparametric Modeling in Generalized Linear Models

Härdle, Wolfgang Karl; Mammen, Enno; Müller, Marlene

doi:10.1080/01621459.1998.10473806

Cited by 54 publications

(45 citation statements)

References 17 publications

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“…However there exists a suitable resampling procedure which is specifically tailored for the testing problem (1.2) and circumvents this drawback. The consistency of this resampling scheme has been shown by Zhu (2005, §5), Delgado & González-Manteiga (2001) and Härdle et al (1998), with different testing procedures for the partial linear model hypothesis (1.2). In practical terms the resampling is implemented as follows: Conditionally on the observations {y j , x j , z j } n j=1 , fit the model according to H 0 , yielding residuals { ε j } n j=1 , and calculate the corresponding value, say T , for the test statistic.…”

Section: Bootstrap Proceduresmentioning

confidence: 95%

Validation tests for semi-parametric models

Meintanis

Einbeck

2013

Journal of Statistical Computation and Simulation

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Section: Bootstrap Proceduresmentioning

confidence: 95%

Validation tests for semi-parametric models

Meintanis

Einbeck

2013

Journal of Statistical Computation and Simulation

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“…Taking the truncated spectrum into the frequency domain results in a power spectrum that is dominated strongly by the main features (the bulges) of the reflectance spectrum. A low-dimensional parametric or semiparametric [22,27] non-linear model will suffice to describe these low-frequency features well. However, such models invariably relegate detail at higher frequencies to the residual variance despite the fact that group effects can be statistically significant at higher frequencies.…”

Section: Discussionmentioning

confidence: 99%

An approach for the analysis of vegetation spectra using non-linear mixed modeling of truncated power spectra

et al. 2004

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-Analysis of vegetation spectra is often characterized by an adverse ratio of sample size to number of wavelengths. A reduction in the dimensionality of the spectra is needed to ensure consistent estimates. We propose a reduction based on a non-linear mixed modeling of power spectra transforms of truncated Fourier series representations of vegetation spectra. Two sets of foliage spectral data obtained from balsam fir (Abies balsamea) exposed to different silvicultural regimes and three eucalypt species (Eucalyptus spp.) demonstrate the method. Only the first 42 frequencies in a power spectrum contributed significantly to the variance of a spectrum. Power spectra were dominated by a small number of low frequencies; the influence of frequency was described well by an exponentiated quadratic polynomial model with significant fixed and random effects. Model parameters can be subject to physiological inference and hypothesis testing. nonlinear-mixed model / Fourier transform / power spectra / hypothesis testing / classificationRésumé -Méthode d'analyse des spectres de végétation par modélisation mixte non linéaire des spectres de puissance tronqués. L'analyse des spectres de végétation est souvent caractérisée par un rapport négatif entre la taille de l'échantillon et le nombre de longueurs d'ondes. Une réduction de la dimension des spectres est nécessaire pour garantir des estimations uniformes. Nous proposons une réduction fondée sur une modélisation mixte non linéaire des transformées de puissance spectrale des représentations de séries de Fourier tronquées visant des spectres de végétation. Pour ce faire, nous utilisons deux ensembles de données spectrales du feuillage de sapins baumiers (Abies balsamea) exposés à différents traitements sylvicoles et de trois espèces d'eucalyptus (Eucalyptus spp.). Seules les 42 premières fréquences de puissance spectrale ont contribué de façon appréciable à sa variance. Un petit nombre de basses fréquences dominaient les puissances spectriques ; l'effet de la fréquence a été bien décrit à l'aide d'un modèle polynomial quadratique d'exponentiation comportant des effets fixes et aléatoires appréciables. Les paramètres du modèle peuvent faire l'objet d'analyse de l'hypothèse et d'une inférence physiologique. modèle mixte non-linéaire / transformation Fourier / répartition spectrale / tests des hypothèses / classification

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“…Inference is then made through the marginal likelihood of the semi-continuous data. Hypothesis testing on variance components or smoothing parameters, or more generally on nonparametric functions in semi-parametric regression, has been investigated (Hardle et al 1998;Zhang and Lin 2003;Claeskens 2004;Liu et al 2005;Crainiceanu et al 2005;Fan and Jiang 2007;Jose Lombardia and Sperlich 2008;Kauermann et al 2009). We choose the likelihood ratio based test, which has been shown to be more powerful in the literature.…”

Section: Penalized Estimation and Determination Of Proportionalitymentioning

confidence: 99%

Determination of proportionality in two-part models and analysis of Multi-Ethnic Study of Atherosclerosis (MESA)

Liu

Kronmal

Zhou

et al. 2011

Statistics and Its Interface

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In MESA (Multi-Ethnic Study of Atherosclerosis), it is of interest to model the development and progression of CAC (coronary artery calcium). With about half of the CAC scores equal to zero and the rest continuously distributed, semiparametric two-part models are needed. Our main interest lies in determining the (partial) proportionality between the two covariate effects in twopart models. Such an investigation can provide important information on the mechanisms underlying CAC development. We propose a novel approach, which consists of penalized maximum likelihood estimation and a step-wise hypothesis testing procedure to determine proportionality. Simulation shows satisfactory performance of the proposed approach. Analysis of MESA suggests that proportionality holds for all covariates except LDL and HDL.

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Testing Parametric versus Semiparametric Modeling in Generalized Linear Models

Cited by 54 publications

References 17 publications

Validation tests for semi-parametric models

Validation tests for semi-parametric models

An approach for the analysis of vegetation spectra using non-linear mixed modeling of truncated power spectra

Determination of proportionality in two-part models and analysis of Multi-Ethnic Study of Atherosclerosis (MESA)

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