109,455 research outputs found
Estimation for an additive growth curve model with orthogonal design matrices
An additive growth curve model with orthogonal design matrices is proposed in
which observations may have different profile forms. The proposed model allows
us to fit data and then estimate parameters in a more parsimonious way than the
traditional growth curve model. Two-stage generalized least-squares estimators
for the regression coefficients are derived where a quadratic estimator for the
covariance of observations is taken as the first-stage estimator. Consistency,
asymptotic normality and asymptotic independence of these estimators are
investigated. Simulation studies and a numerical example are given to
illustrate the efficiency and parsimony of the proposed model for model
specifications in the sense of minimizing Akaike's information criterion (AIC).Comment: Published in at http://dx.doi.org/10.3150/10-BEJ315 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Boosting Functional Response Models for Location, Scale and Shape with an Application to Bacterial Competition
We extend Generalized Additive Models for Location, Scale, and Shape (GAMLSS)
to regression with functional response. This allows us to simultaneously model
point-wise mean curves, variances and other distributional parameters of the
response in dependence of various scalar and functional covariate effects. In
addition, the scope of distributions is extended beyond exponential families.
The model is fitted via gradient boosting, which offers inherent model
selection and is shown to be suitable for both complex model structures and
highly auto-correlated response curves. This enables us to analyze bacterial
growth in \textit{Escherichia coli} in a complex interaction scenario,
fruitfully extending usual growth models.Comment: bootstrap confidence interval type uncertainty bounds added; minor
changes in formulation
Estimation of COVID-19 spread curves integrating global data and borrowing information
Currently, novel coronavirus disease 2019 (COVID-19) is a big threat to
global health. The rapid spread of the virus has created pandemic, and
countries all over the world are struggling with a surge in COVID-19 infected
cases. There are no drugs or other therapeutics approved by the US Food and
Drug Administration to prevent or treat COVID-19: information on the disease is
very limited and scattered even if it exists. This motivates the use of data
integration, combining data from diverse sources and eliciting useful
information with a unified view of them. In this paper, we propose a Bayesian
hierarchical model that integrates global data for real-time prediction of
infection trajectory for multiple countries. Because the proposed model takes
advantage of borrowing information across multiple countries, it outperforms an
existing individual country-based model. As fully Bayesian way has been
adopted, the model provides a powerful predictive tool endowed with uncertainty
quantification. Additionally, a joint variable selection technique has been
integrated into the proposed modeling scheme, which aimed to identify possible
country-level risk factors for severe disease due to COVID-19
Design Issues for Generalized Linear Models: A Review
Generalized linear models (GLMs) have been used quite effectively in the
modeling of a mean response under nonstandard conditions, where discrete as
well as continuous data distributions can be accommodated. The choice of design
for a GLM is a very important task in the development and building of an
adequate model. However, one major problem that handicaps the construction of a
GLM design is its dependence on the unknown parameters of the fitted model.
Several approaches have been proposed in the past 25 years to solve this
problem. These approaches, however, have provided only partial solutions that
apply in only some special cases, and the problem, in general, remains largely
unresolved. The purpose of this article is to focus attention on the
aforementioned dependence problem. We provide a survey of various existing
techniques dealing with the dependence problem. This survey includes
discussions concerning locally optimal designs, sequential designs, Bayesian
designs and the quantile dispersion graph approach for comparing designs for
GLMs.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Fluctuation analysis: can estimates be trusted?
The estimation of mutation probabilities and relative fitnesses in
fluctuation analysis is based on the unrealistic hypothesis that the
single-cell times to division are exponentially distributed. Using the
classical Luria-Delbr\"{u}ck distribution outside its modelling hypotheses
induces an important bias on the estimation of the relative fitness. The model
is extended here to any division time distribution. Mutant counts follow a
generalization of the Luria-Delbr\"{u}ck distribution, which depends on the
mean number of mutations, the relative fitness of normal cells compared to
mutants, and the division time distribution of mutant cells. Empirical
probability generating function techniques yield precise estimates both of the
mean number of mutations and the relative fitness of normal cells compared to
mutants. In the case where no information is available on the division time
distribution, it is shown that the estimation procedure using constant division
times yields more reliable results. Numerical results both on observed and
simulated data are reported
Measurement and Nature of Absolute Poverty in Least Developed Countries
This paper provides new national accounts consistent poverty estimates for low-income countries. The properties of the new estimates are compared to the existing estimates by the World Bank based on household survey means. We also use the new estimates to reflect on the recent controversies regarding the relationship between economic growth and poverty reduction. It is argued that the controversy is mainly due to the lack of distinction between what one can refer to as ‘generalized extreme poverty’ in low-income countries and the more ‘normal’ poverty situations in higher income economies
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Estimating Mean and Covariance Structure with Reweighted Least Squares
Does Reweighted Least Squares (RLS) perform better in small samples than maximum likelihood (ML) for mean and covariance structure? ML statistics in covariance structure analysis are based on the asymptotic normality assumption; however, actual applications of structural equation modeling (SEM) in social and behavioral science research usually involve small samples. It has been found that chi-square tests often incorrectly over-reject the null hypothesis: Σ=Σ(θ), because when sample is small the sample covariance matrix becomes ill-conditioned and entails unstable estimates. In certain SEM models, the vector of parameter must contain both means, variances and covariances. Yet, whether RLS also works in mean and covariance structure remains unexamined. This research is an extended examination of reweighted least squares in mean and covariance structure. Specifically, we replace biased covariance matrix in traditional GLS function (Browne, 1974) with the unbiased sample covariance matrix that derives from ML estimation. Moreover, under the assumption of multivariate normality, a Monte Carlo simulation study was carried out to examine the statistical performance as compared with ML methods in different sample sizes. Based on empirical rejection frequencies and empirical averages of test statistic, this study shows that RLS performs much better than ML in mean and covariance structure models when sample sizes are small
Estimation in a growth study with irregular measurement times
Between 1982 and 1988 a growth study was carried out at the Division of Pediatric Oncology of the University Hospital of Groningen. A special feature of the project was that sample sizes are small and that ages at entry may be very different. In addition the intended design was not fully complied with. This paper highlights some aspects of the statistical analysis which is based on (1) reference scores, (2) statistical procedures allowing for an irregular pattern of measurement times caused by missing data and shifted measurement times
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