2,601 research outputs found
MATS: Inference for potentially Singular and Heteroscedastic MANOVA
In many experiments in the life sciences, several endpoints are recorded per
subject. The analysis of such multivariate data is usually based on MANOVA
models assuming multivariate normality and covariance homogeneity. These
assumptions, however, are often not met in practice. Furthermore, test
statistics should be invariant under scale transformations of the data, since
the endpoints may be measured on different scales. In the context of
high-dimensional data, Srivastava and Kubokawa (2013) proposed such a test
statistic for a specific one-way model, which, however, relies on the
assumption of a common non-singular covariance matrix. We modify and extend
this test statistic to factorial MANOVA designs, incorporating general
heteroscedastic models. In particular, our only distributional assumption is
the existence of the group-wise covariance matrices, which may even be
singular. We base inference on quantiles of resampling distributions, and
derive confidence regions and ellipsoids based on these quantiles. In a
simulation study, we extensively analyze the behavior of these procedures.
Finally, the methods are applied to a data set containing information on the
2016 presidential elections in the USA with unequal and singular empirical
covariance matrices
A semiparametric regression model for paired longitudinal outcomes with application in childhood blood pressure development
This research examines the simultaneous influences of height and weight on
longitudinally measured systolic and diastolic blood pressure in children.
Previous studies have shown that both height and weight are positively
associated with blood pressure. In children, however, the concurrent increases
of height and weight have made it all but impossible to discern the effect of
height from that of weight. To better understand these influences, we propose
to examine the joint effect of height and weight on blood pressure. Bivariate
thin plate spline surfaces are used to accommodate the potentially nonlinear
effects as well as the interaction between height and weight. Moreover, we
consider a joint model for paired blood pressure measures, that is, systolic
and diastolic blood pressure, to account for the underlying correlation between
the two measures within the same individual. The bivariate spline surfaces are
allowed to vary across different groups of interest. We have developed related
model fitting and inference procedures. The proposed method is used to analyze
data from a real clinical investigation.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS567 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Testing the suitability of polynomial models in errors-in-variables problems
A low-degree polynomial model for a response curve is used commonly in
practice. It generally incorporates a linear or quadratic function of the
covariate. In this paper we suggest methods for testing the goodness of fit of
a general polynomial model when there are errors in the covariates. There, the
true covariates are not directly observed, and conventional bootstrap methods
for testing are not applicable. We develop a new approach, in which
deconvolution methods are used to estimate the distribution of the covariates
under the null hypothesis, and a ``wild'' or moment-matching bootstrap argument
is employed to estimate the distribution of the experimental errors (distinct
from the distribution of the errors in covariates). Most of our attention is
directed at the case where the distribution of the errors in covariates is
known, although we also discuss methods for estimation and testing when the
covariate error distribution is estimated. No assumptions are made about the
distribution of experimental error, and, in particular, we depart substantially
from conventional parametric models for errors-in-variables problems.Comment: Published in at http://dx.doi.org/10.1214/009053607000000361 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Nonparametric estimation of mean-squared prediction error in nested-error regression models
Nested-error regression models are widely used for analyzing clustered data.
For example, they are often applied to two-stage sample surveys, and in biology
and econometrics. Prediction is usually the main goal of such analyses, and
mean-squared prediction error is the main way in which prediction performance
is measured. In this paper we suggest a new approach to estimating mean-squared
prediction error. We introduce a matched-moment, double-bootstrap algorithm,
enabling the notorious underestimation of the naive mean-squared error
estimator to be substantially reduced. Our approach does not require specific
assumptions about the distributions of errors. Additionally, it is simple and
easy to apply. This is achieved through using Monte Carlo simulation to
implicitly develop formulae which, in a more conventional approach, would be
derived laboriously by mathematical arguments.Comment: Published at http://dx.doi.org/10.1214/009053606000000579 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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