33,271 research outputs found
On nonparametric estimation of a mixing density via the predictive recursion algorithm
Nonparametric estimation of a mixing density based on observations from the
corresponding mixture is a challenging statistical problem. This paper surveys
the literature on a fast, recursive estimator based on the predictive recursion
algorithm. After introducing the algorithm and giving a few examples, I
summarize the available asymptotic convergence theory, describe an important
semiparametric extension, and highlight two interesting applications. I
conclude with a discussion of several recent developments in this area and some
open problems.Comment: 22 pages, 5 figures. Comments welcome at
https://www.researchers.one/article/2018-12-
Locally stationary long memory estimation
There exists a wide literature on modelling strongly dependent time series
using a longmemory parameter d, including more recent work on semiparametric
wavelet estimation. As a generalization of these latter approaches, in this
work we allow the long-memory parameter d to be varying over time. We embed our
approach into the framework of locally stationary processes. We show weak
consistency and a central limit theorem for our log-regression wavelet
estimator of the time-dependent d in a Gaussian context. Both simulations and a
real data example complete our work on providing a fairly general approach
Forecasting and prequential validation for time varying meta-elliptical distributions
We consider forecasting and prequential (predictive sequential) validation of meta-elliptical distributions with time varying parameters. Using the weak prequential principle of Dawid, we conduct model validation avoiding nuisance parameter problems. Results rely on the structure of meta-elliptical distributions and we allow for discontinuities in the marginals and time varying parameters. We illustrate the ideas of the paper using a large data set of 16 commodity prices
Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC)
We develop a novel advanced Particle Markov chain Monte Carlo algorithm that
is capable of sampling from the posterior distribution of non-linear state
space models for both the unobserved latent states and the unknown model
parameters. We apply this novel methodology to five population growth models,
including models with strong and weak Allee effects, and test if it can
efficiently sample from the complex likelihood surface that is often associated
with these models. Utilising real and also synthetically generated data sets we
examine the extent to which observation noise and process error may frustrate
efforts to choose between these models. Our novel algorithm involves an
Adaptive Metropolis proposal combined with an SIR Particle MCMC algorithm
(AdPMCMC). We show that the AdPMCMC algorithm samples complex, high-dimensional
spaces efficiently, and is therefore superior to standard Gibbs or Metropolis
Hastings algorithms that are known to converge very slowly when applied to the
non-linear state space ecological models considered in this paper.
Additionally, we show how the AdPMCMC algorithm can be used to recursively
estimate the Bayesian Cram\'er-Rao Lower Bound of Tichavsk\'y (1998). We derive
expressions for these Cram\'er-Rao Bounds and estimate them for the models
considered. Our results demonstrate a number of important features of common
population growth models, most notably their multi-modal posterior surfaces and
dependence between the static and dynamic parameters. We conclude by sampling
from the posterior distribution of each of the models, and use Bayes factors to
highlight how observation noise significantly diminishes our ability to select
among some of the models, particularly those that are designed to reproduce an
Allee effect
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