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11.
Gabriela Beganu 《Statistical Methods and Applications》2007,16(3):347-356
It is known that the Henderson Method III (Biometrics 9:226–252, 1953) is of special interest for the mixed linear models
because the estimators of the variance components are unaffected by the parameters of the fixed factor (or factors). This
article deals with generalizations and minor extensions of the results obtained for the univariate linear models. A MANOVA
mixed model is presented in a convenient form and the covariance components estimators are given on finite dimensional linear
spaces. The results use both the usual parametric representations and the coordinate-free approach of Kruskal (Ann Math Statist
39:70–75, 1968) and Eaton (Ann Math Statist 41:528–538, 1970). The normal equations are generalized and it is given a necessary
and sufficient condition for the existence of quadratic unbiased estimators for covariance components in the considered model. 相似文献
12.
This paper develops inference for the significance of features such as peaks and valleys observed in additive modeling through
an extension of the SiZer-type methodology of Chaudhuri and Marron (1999) and Godtliebsen et al. (2002, 2004) to the case
where the outcome is discrete. We consider the problem of determining the significance of features such as peaks or valleys
in observed covariate effects both for the case of additive modeling where the main predictor of interest is univariate as
well as the problem of studying the significance of features such as peaks, inclines, ridges and valleys when the main predictor
of interest is geographical location. We work with low rank radial spline smoothers to allow to the handling of sparse designs
and large sample sizes. Reducing the problem to a Generalised Linear Mixed Model (GLMM) framework enables derivation of simulation-based
critical value approximations and guards against the problem of multiple inferences over a range of predictor values. Such
a reduction also allows for easy adjustment for confounders including those which have an unknown or complex effect on the
outcome. A simulation study indicates that our method has satisfactory power. Finally, we illustrate our methodology on several
data sets. 相似文献
13.
Catriona M. Queen Ben J. Wright Casper J. Albers 《Australian & New Zealand Journal of Statistics》2007,49(3):221-239
The problem of modelling multivariate time series of vehicle counts in traffic networks is considered. It is proposed to use a model called the linear multiregression dynamic model (LMDM). The LMDM is a multivariate Bayesian dynamic model which uses any conditional independence and causal structure across the time series to break down the complex multivariate model into simpler univariate dynamic linear models. The conditional independence and causal structure in the time series can be represented by a directed acyclic graph (DAG). The DAG not only gives a useful pictorial representation of the multivariate structure, but it is also used to build the LMDM. Therefore, eliciting a DAG which gives a realistic representation of the series is a crucial part of the modelling process. A DAG is elicited for the multivariate time series of hourly vehicle counts at the junction of three major roads in the UK. A flow diagram is introduced to give a pictorial representation of the possible vehicle routes through the network. It is shown how this flow diagram, together with a map of the network, can suggest a DAG for the time series suitable for use with an LMDM. 相似文献
14.
This paper shows how to construct confidence bands for the difference between two simple linear regression lines. These confidence bands provide directly the information on the magnitude of the difference between the regression lines over an interval of interest and, as a by-product, can be used as a formal test of the difference between the two regression lines. Various different shapes of confidence bands are illustrated, and particular attention is paid towards confidence bands whose construction only involves critical points from standard distributions so that they are consequently easy to construct. 相似文献
15.
16.
When we want to compare two designs we usually assume the standard linear model with uncorrelated observations. In this paper we use the comparison method proposed by Ghosh & Shen (2006) to compare three level orthogonal arrays with 18, 27 and 36 runs under a possible presence of correlation in observations. 相似文献
17.
Harriet Namata Ziv Shkedy Christel Faes Marc Aerts Geert Molenberghs Heide Theeten Pierre Van Damme Philippe Beutels 《Journal of applied statistics》2007,34(8):923-939
Based on sero-prevalence data of rubella, mumps in the UK and varicella in Belgium, we show how the force of infection, the age-specific rate at which susceptible individuals contract infection, can be estimated using generalized linear mixed models (McCulloch & Searle, 2001). Modelling the dependency of the force of infection on age by penalized splines, which involve fixed and random effects, allows us to use generalized linear mixed models techniques to estimate both the cumulative probability of being infected before a given age and the force of infection. Moreover, these models permit an automatic selection of the smoothing parameter. The smoothness of the estimated force of infection can be influenced by the number of knots and the degree of the penalized spline used. To determine these, a different number of knots and different degrees are used and the results are compared to establish this sensitivity. Simulations with a different number of knots and polynomial spline bases of different degrees suggest - for estimating the force of infection from serological data - the use of a quadratic penalized spline based on about 10 knots. 相似文献
18.
In recent issues of this journal it has been asserted in two papers that the use of h-likelihood is wrong, in the sense of
giving unsatisfactory estimates of some parameters for binary data (Kuk and Cheng, 1999; Waddington and Thompson, 2004) or
theoretically unsound (Kuk and Cheng, 1999). We wish to refute both these assertions. 相似文献
19.
宣培才 《绍兴文理学院学报》1992,(6)
本文推广了的结果,主要研究了一类Ismail-May算子线性组合的同时逼近问题,在一致通近意义下,给出了逼近的正定理、逆定理及非最优逼近阶的特征刻划. 相似文献
20.
In this paper we define a class of unbalanced designs, denoted by Ck,s,t, for estimating the components of variance in a k-stage nested random effects linear model. This class contains many of the designs proposed in the literature for nested components of variance models. We focus on the three-state model and discuss the determination of locally optimal designs within this class using a systematic computer search. For large sample sizes we show that approximate optimal designs may be obtained using a limit argument combined with numerical optimization. A comparison of our designs with previously published designs suggests that, in many cases, our designs result in substantial gains in efficiency. 相似文献