7,313 research outputs found
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Empirical likelihood estimation of the spatial quantile regression
The spatial quantile regression model is a useful and flexible model for analysis of empirical problems with spatial dimension. This paper introduces an alternative estimator for this model. The properties of the proposed estimator are discussed in a comparative perspective with regard to the other available estimators. Simulation evidence on the small sample properties of the proposed estimator is provided. The proposed estimator is feasible and preferable when the model contains multiple spatial weighting matrices. Furthermore, a version of the proposed estimator based on the exponentially tilted empirical likelihood could be beneficial if model misspecification is suspect
Variable Selection for Generalized Linear Mixed Models by L1-Penalized Estimation
Generalized linear mixed models are a widely used tool for modeling longitudinal data. However, their use is typically restricted to few covariates, because the presence of many predictors yields unstable estimates. The presented approach to the fitting of generalized linear mixed
models includes an L1-penalty term that enforces variable selection and shrinkage simultaneously. A gradient ascent algorithm is proposed that allows to maximize the penalized loglikelihood yielding models with reduced complexity. In contrast to common procedures it can be used in high-dimensional settings where a large number of otentially influential explanatory variables is available. The method is investigated in simulation studies and illustrated by use of real data sets
Variable Selection for Generalized Linear Mixed Models by L1-Penalized Estimation
Generalized linear mixed models are a widely used tool for modeling longitudinal data. However, their use is typically restricted to few covariates, because the presence of many predictors yields unstable estimates. The presented approach to the fitting of generalized linear mixed
models includes an L1-penalty term that enforces variable selection and shrinkage simultaneously. A gradient ascent algorithm is proposed that allows to maximize the penalized loglikelihood yielding models with reduced complexity. In contrast to common procedures it can be used in high-dimensional settings where a large number of otentially influential explanatory variables is available. The method is investigated in simulation studies and illustrated by use of real data sets
Civil war risk in democratic and non-democratic neighborhoods
This study questions the extent to which domestic conflict is influenced by national, regional, and international relationships. It is designed to answer specific questions relating to the effects of neighboring characteristics on a state's risk of conflict and instability: What is the interaction between neighboring conflict and political disorder? Do democratic neighborhoods have different conflict trajectories than non-democratic neighborhoods and if so, where and why? Given that most poor countries are located in poor and conflictual neighborhoods, to what extent is there a relationship between poverty and political disorder in different regime neighborhoods? Using spatial lag terms to specify neighboring regime characteristics and multilevel models to differentiate between explanatory levels, this study reiterates the importance of domestic and neighboring factors in promoting or diminishing the risk of instability and conflict. However, the pronounced negative effects of autocratic and anocratic neighborhoods are mitigated by a growing domestic GDP. This study also finds that democratic neighborhoods are more stable, regardless of income level. Research presented here is unique in its contribution on how regime type is a significant development indicator, which in turn is salient in determining the risks of civil war across states.Peace&Peacekeeping,Population Policies,Services&Transfers to Poor,Social Conflict and Violence,Post Conflict Reintegration
Discussion paper. Conditional growth charts
Growth charts are often more informative when they are customized per
subject, taking into account prior measurements and possibly other covariates
of the subject. We study a global semiparametric quantile regression model that
has the ability to estimate conditional quantiles without the usual
distributional assumptions. The model can be estimated from longitudinal
reference data with irregular measurement times and with some level of
robustness against outliers, and it is also flexible for including covariate
information. We propose a rank score test for large sample inference on
covariates, and develop a new model assessment tool for longitudinal growth
data. Our research indicates that the global model has the potential to be a
very useful tool in conditional growth chart analysis.Comment: This paper discussed in: [math/0702636], [math/0702640],
[math/0702641], [math/0702642]. Rejoinder in [math.ST/0702643]. Published at
http://dx.doi.org/10.1214/009053606000000623 in the Annals of Statistics
(http://www.imstat.org/aos/) by the Institute of Mathematical Statistics
(http://www.imstat.org
First Observational Tests of Eternal Inflation: Analysis Methods and WMAP 7-Year Results
In the picture of eternal inflation, our observable universe resides inside a
single bubble nucleated from an inflating false vacuum. Many of the theories
giving rise to eternal inflation predict that we have causal access to
collisions with other bubble universes, providing an opportunity to confront
these theories with observation. We present the results from the first
observational search for the effects of bubble collisions, using cosmic
microwave background data from the WMAP satellite. Our search targets a generic
set of properties associated with a bubble collision spacetime, which we
describe in detail. We use a modular algorithm that is designed to avoid a
posteriori selection effects, automatically picking out the most promising
signals, performing a search for causal boundaries, and conducting a full
Bayesian parameter estimation and model selection analysis. We outline each
component of this algorithm, describing its response to simulated CMB skies
with and without bubble collisions. Comparing the results for simulated bubble
collisions to the results from an analysis of the WMAP 7-year data, we rule out
bubble collisions over a range of parameter space. Our model selection results
based on WMAP 7-year data do not warrant augmenting LCDM with bubble
collisions. Data from the Planck satellite can be used to more definitively
test the bubble collision hypothesis.Comment: Companion to arXiv:1012.1995. 41 pages, 23 figures. v2: replaced with
version accepted by PRD. Significant extensions to the Bayesian pipeline to
do the full-sky non-Gaussian source detection problem (previously restricted
to patches). Note that this has changed the normalization of evidence values
reported previously, as full-sky priors are now employed, but the conclusions
remain unchange
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