Robust estimation in the multivariate normal model

2016 ◽  
Vol 36 (1-2) ◽  
pp. 53
Author(s):  
Agnieszka Kulawik ◽  
Stefan Zontek
Keyword(s):  
Robust Estimation ◽  
Normal Model ◽  
Multivariate Normal ◽  
Multivariate Normal Model

Longitudinal analysis of lung function growth in healthy children and adolescents

1991 ◽  
Vol 70 (2) ◽  
pp. 770-777 ◽  
Author(s):  
J. L. Hopper ◽  
M. E. Hibbert ◽  
G. T. Macaskill ◽  
P. D. Phelan ◽  
L. I. Landau
Keyword(s):  
Lung Function ◽  
Early Detection ◽  
Vital Capacity ◽  
Forced Expiratory Volume ◽  
Healthy Children ◽  
Normal Model ◽  
Multivariate Normal ◽  
Pronounced Increase ◽  
Multivariate Normal Model ◽  
Healthy Lung

Lung function and height in 242 8-yr-old and 299 12-yr-old children without known or suspected predisposition to lung disease were measured annually over 6 and 8 yr, respectively. Growth of forced expiratory volume in 1 s (FEV1), vital capacity, and expiratory flow after expiring 50% of vital capacity were statistically modeled by age and height by use of a multivariate normal model for longitudinal data. This method has the flexibility to fit an appropriate (not necessarily linear) mathematical description of average lung function while concurrently modeling the covariance between measures on the same individual. Differences in lung function growth between girls and boys, pre- and post-puberty, showed that girls had a steadier though less pronounced increase in lung function with height. In boys, before puberty there was deficit in lung volume relative to height (not evident in girls), which was compensated for by rapid growth after puberty. The standard error of FEV1 predictions based on current height and age were more than halved when measurements of FEV1, age, and height taken 1 yr before were incorporated. We found evidence for dysanaptic growth in childhood. Fitted models have application to early detection of departures from healthy lung function.

scholarly journals The quantitative genetic consequences of pleiotropy under stabilizing and directional selection.

Genetics ◽  
1990 ◽  
Vol 125 (1) ◽  
pp. 207-213 ◽  
Author(s):  
M Slatkin ◽  
S A Frank
Keyword(s):  
Directional Selection ◽  
Stabilizing Selection ◽  
Normal Model ◽  
Multivariate Normal ◽  
Genetic Covariance ◽  
Phenotypic Characters ◽  
House Of Cards ◽  
Quantitative Genetic ◽  
Stepwise Mutation ◽  
Multivariate Normal Model

Abstract The independence of two phenotypic characters affected by both pleiotropic and nonpleiotropic mutations is investigated using a generalization of M. Slatkin's stepwise mutation model of 1987. The model is used to determine whether predictions of either the multivariate normal model introduced in 1980 by R. Lande or the house-of-cards model introduced in 1985 by M. Turelli can be regarded as typical of models that are intermediate between them. We found that, under stabilizing selection, the variance of one character at equilibrium may depend on the strength of stabilizing selection on the other character (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the types of mutations that can occur. Similarly, under directional selection, the genetic covariance between two characters may increase substantially (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the kinds of mutations that are assumed to occur. Hence, even for the simple model we consider, neither the house-of-cards nor the multivariate normal model can be used to make predictions, making it unlikely that either could be used to draw general conclusions about more complex and realistic models.

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