Testing Parametric versus Semiparametric Modelling in Generalized Linear Models

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

doi:10.2139/ssrn.544

Cited by 21 publications

(24 citation statements)

References 22 publications

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“…Ovary development was analysed using the generalized linear/nonlinear models (GLZ) module in Statistica 9.0 (Institute 2004), specifying a Poisson distribution and a log link function, which is a semi-parametric statistical test (Härdle et al 1996). Colony was a random effect and experimental group was a fixed effect.…”

Section: Discussionmentioning

confidence: 99%

Reproduction of rebel workers in honeybee (Apis mellifera) colonies

2017

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-The honeybee is one of several eusocial species in which the queen is typically the only reproductive member of the colony; worker reproduction is mostly restricted to queenless colonies. Because workers cannot mate, they lay unfertilized eggs, which develop into males. A recent study showed that in queenless colonies, which arise after swarming, worker larvae develop into rebel workers that have greater reproductive potential than do workers reared in queenright colonies, as measured by the number of ovarioles and degree of ovary activation. However, there was no evidence that rebels had an opportunity to produce male offspring. Here, we show for the first time that rebel workers not only activate their ovaries but also produce significantly more male offspring in queenright colonies than do normal workers. Moreover, our results show that the level of rebel reproduction in queenright colonies is similar to the reproduction of normal workers in queenless colonies. This finding suggests that the ultimate factor favouring the evolution of the rebel strategy is the decrease in relatedness between the old-generation workers and the new queen's offspring that occurs after queen exchange at swarming.Apis mellifera / rebel workers / worker reproduction / kin selection

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Section: Discussionmentioning

confidence: 99%

Reproduction of rebel workers in honeybee (Apis mellifera) colonies

2017

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“…The fitted spline is then obtained as the BLUE (best linear unbiased) and BLUP (best linear unbiased predictor) solutions of the mixed model (see [13]) where Ub is the linear part and the smooth term is approximated by Xβ + Zξ. For our study 1000 random vectors were generated from (18) for each value of edf = 2, 4,6,8,10,15,20,25,30 with the corresponding σ 2 ξ . We took X = (1, x), x = (1, 2, .…”

Section: A Simulation Studymentioning

confidence: 99%

“…Statistical inference of semiparametric regression models have been considered by several authors. However, most of the references concentrate on the methods for independent data (see e.g [1,2,5] and [7] for linear models and [10] and [11] for generalized linear models). For dependent data, we may refer to [20] who have considered statistical inference under the semiparametric additive model framework.…”

Section: Introductionmentioning

confidence: 99%

Testing linearity in semiparametric regression models

Nummi

Pan

Mesue

2013

Statistics and Its Interface

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One of the fundamental assumptions of a basic multiple linear regression model is that the contribution of each of the model terms is strictly linear. In many cases, this may be an excessive simplification of the complicated relationships. Moreover, it may be difficult or impossible to test the hypothesized model against all possible kinds of relevant alternative models. Therefore, tests that perform well under more general circumstances are also required. This paper considers the semiparametric model, where the contribution of one of the model terms may not be strictly linear, and also proposes an exact F-test for the situation. The method also allows dependent error terms. The performance of the proposed test is illustrated by simulation experiments and in real air pollution and health data.

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“…In similar cases the normal approximation does not perform well (see e.g. Hiirdle, Mammen and Miiller, 1998), we thus propose using the boots trap for the calculation of critical values of the test statistic R. The boots trap estimate of the distribution of R is given by the conditional distribution of the test statistic R*, where R* is defined as follows.…”

Section: Bootstrap Applications In Generalized Additive Modelsmentioning

confidence: 99%

“…Equations (A3.11) and (A3.12) follow from a slight modification of Lemma A3.3 and Corollary A3.4 in Hardle, Mammen and Miiller (1998). There it has been assumed that the likelihood is maximized for {3 in a neighborhood of {3o with radius PI, see assumption (A7) in Hardle, Mammen and MUller (1998).…”

Section: I3eb N Nmentioning

confidence: 99%

Bootstrap Inference in Semiparametric Generalized Additive Models

Härdle

Huet²,

Mammen

et al. 2004

Econ. Theory

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Semiparametric generalized additive models are a powerful tool in quantitative econometrics. With response Y, covariates X,T, the considered model is E(Y |X;T) = G{XTβ + α + m1(T1) + ··· + md(Td)}. Here, G is a known link, α and β are unknown parameters, and m1,…,md are unknown (smooth) functions of possibly higher dimensional covariates T1,…,Td. Estimates of m1,…,md, α, and β are presented, and asymptotic distributions are given for both the nonparametric and the parametric part. The main focus of the paper is application of bootstrap methods. It is shown how bootstrap can be used for bias correction, hypothesis testing (e.g., component-wise analysis), and the construction of uniform confidence bands. Further, bootstrap tests for model specification and parametrization are given, in particular for testing additivity and link function specification. The practical performance of the methods is illustrated in a simulation study.This research was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 373 “Quantifikation und Simulation ökonomischer Prozesse,” Humboldt-Universität zu Berlin, DFG project MA 1026/6-2, the Spanish “Dirección General de Enseñanza Superior,” no. BEC2001-1270, and the grant “Nonparametric methods in finance and insurance” from the Danish Social Science Research Council. We thank Marlene Müller, Oliver Linton, and two anonymous referees for helpful discussion.

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Testing Parametric versus Semiparametric Modelling in Generalized Linear Models

Cited by 21 publications

References 22 publications

Reproduction of rebel workers in honeybee (Apis mellifera) colonies

Reproduction of rebel workers in honeybee (Apis mellifera) colonies

Testing linearity in semiparametric regression models

Bootstrap Inference in Semiparametric Generalized Additive Models

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