1,102 research outputs found
Markov-switching generalized additive models
We consider Markov-switching regression models, i.e. models for time series
regression analyses where the functional relationship between covariates and
response is subject to regime switching controlled by an unobservable Markov
chain. Building on the powerful hidden Markov model machinery and the methods
for penalized B-splines routinely used in regression analyses, we develop a
framework for nonparametrically estimating the functional form of the effect of
the covariates in such a regression model, assuming an additive structure of
the predictor. The resulting class of Markov-switching generalized additive
models is immensely flexible, and contains as special cases the common
parametric Markov-switching regression models and also generalized additive and
generalized linear models. The feasibility of the suggested maximum penalized
likelihood approach is demonstrated by simulation and further illustrated by
modelling how energy price in Spain depends on the Euro/Dollar exchange rate
Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data
When collections of functional data are too large to be exhaustively
observed, survey sampling techniques provide an effective way to estimate
global quantities such as the population mean function. Assuming functional
data are collected from a finite population according to a probabilistic
sampling scheme, with the measurements being discrete in time and noisy, we
propose to first smooth the sampled trajectories with local polynomials and
then estimate the mean function with a Horvitz-Thompson estimator. Under mild
conditions on the population size, observation times, regularity of the
trajectories, sampling scheme, and smoothing bandwidth, we prove a Central
Limit theorem in the space of continuous functions. We also establish the
uniform consistency of a covariance function estimator and apply the former
results to build confidence bands for the mean function. The bands attain
nominal coverage and are obtained through Gaussian process simulations
conditional on the estimated covariance function. To select the bandwidth, we
propose a cross-validation method that accounts for the sampling weights. A
simulation study assesses the performance of our approach and highlights the
influence of the sampling scheme and bandwidth choice.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ443 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Semiparametric inference in mixture models with predictive recursion marginal likelihood
Predictive recursion is an accurate and computationally efficient algorithm
for nonparametric estimation of mixing densities in mixture models. In
semiparametric mixture models, however, the algorithm fails to account for any
uncertainty in the additional unknown structural parameter. As an alternative
to existing profile likelihood methods, we treat predictive recursion as a
filter approximation to fitting a fully Bayes model, whereby an approximate
marginal likelihood of the structural parameter emerges and can be used for
inference. We call this the predictive recursion marginal likelihood.
Convergence properties of predictive recursion under model mis-specification
also lead to an attractive construction of this new procedure. We show
pointwise convergence of a normalized version of this marginal likelihood
function. Simulations compare the performance of this new marginal likelihood
approach that of existing profile likelihood methods as well as Dirichlet
process mixtures in density estimation. Mixed-effects models and an empirical
Bayes multiple testing application in time series analysis are also considered
Deductive semiparametric estimation in Double-Sampling Designs with application to PEPFAR
Non-ignorable dropout is common in studies with long follow-up time, and it
can bias study results unless handled carefully. A double-sampling design
allocates additional resources to pursue a subsample of the dropouts and find
out their outcomes, which can address potential biases due to non-ignorable
dropout. It is desirable to construct semiparametric estimators for the
double-sampling design because of their robustness properties. However,
obtaining such semiparametric estimators remains a challenge due to the
requirement of the analytic form of the efficient influence function (EIF), the
derivation of which can be ad hoc and difficult for the double-sampling design.
Recent work has shown how the derivation of EIF can be made deductive and
computerizable using the functional derivative representation of the EIF in
nonparametric models. This approach, however, requires deriving the mixture of
a continuous distribution and a point mass, which can itself be challenging for
complicated problems such as the double-sampling design. We propose
semiparametric estimators for the survival probability in double-sampling
designs by generalizing the deductive and computerizable estimation approach.
In particular, we propose to build the semiparametric estimators based on a
discretized support structure, which approximates the possibly continuous
observed data distribution and circumvents the derivation of the mixture
distribution. Our approach is deductive in the sense that it is expected to
produce semiparametric locally efficient estimators within finite steps without
knowledge of the EIF. We apply the proposed estimators to estimating the
mortality rate in a double-sampling design component of the President's
Emergency Plan for AIDS Relief (PEPFAR) program. We evaluate the impact of
double-sampling selection criteria on the mortality rate estimates
Age Dynamics and Economic Growth: Revisiting the Nexus in a Nonparametric Setting.
This paper explores the relationship between the growth rates of per capita income and age- structured population in a non-parametric setting. Analysis in this framework provides us with new insights about the interaction structure: significant non-linear relation between the two and interesting ’direct’ and ’feedback’ effects on growth. Nonlinearity is found to be a major source of growth fluctuations in OECD and non-OECD countries.Age dynamics, Economic growth, Non-parametric panel.
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