3,969 research outputs found
The iterated auxiliary particle filter
We present an offline, iterated particle filter to facilitate statistical
inference in general state space hidden Markov models. Given a model and a
sequence of observations, the associated marginal likelihood L is central to
likelihood-based inference for unknown statistical parameters. We define a
class of "twisted" models: each member is specified by a sequence of positive
functions psi and has an associated psi-auxiliary particle filter that provides
unbiased estimates of L. We identify a sequence psi* that is optimal in the
sense that the psi*-auxiliary particle filter's estimate of L has zero
variance. In practical applications, psi* is unknown so the psi*-auxiliary
particle filter cannot straightforwardly be implemented. We use an iterative
scheme to approximate psi*, and demonstrate empirically that the resulting
iterated auxiliary particle filter significantly outperforms the bootstrap
particle filter in challenging settings. Applications include parameter
estimation using a particle Markov chain Monte Carlo algorithm
Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters
Prediction intervals in State Space models can be obtained by assuming Gaussian innovations
and using the prediction equations of the Kalman filter, where the true parameters are
substituted by consistent estimates. This approach has two limitations. First, it does not
incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of
future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002)
propose to obtain prediction intervals by using a bootstrap procedure that requires the backward
representation of the model. Obtaining this representation increases the complexity of the
procedure and limits its implementation to models for which it exists. The bootstrap procedure
proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are
obtained for the prediction errors instead of for the observations. In this paper, we propose a
bootstrap procedure for constructing prediction intervals in State Space models that does not
need the backward representation of the model and is based on obtaining the intervals directly
for the observations. Therefore, its application is much simpler, without loosing the good
behavior of bootstrap prediction intervals. We study its finite sample properties and compare
them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level
Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction
intervals for future values of a real time series
Adaptive Quantizers for Estimation
In this paper, adaptive estimation based on noisy quantized observations is
studied. A low complexity adaptive algorithm using a quantizer with adjustable
input gain and offset is presented. Three possible scalar models for the
parameter to be estimated are considered: constant, Wiener process and Wiener
process with deterministic drift. After showing that the algorithm is
asymptotically unbiased for estimating a constant, it is shown, in the three
cases, that the asymptotic mean squared error depends on the Fisher information
for the quantized measurements. It is also shown that the loss of performance
due to quantization depends approximately on the ratio of the Fisher
information for quantized and continuous measurements. At the end of the paper
the theoretical results are validated through simulation under two different
classes of noise, generalized Gaussian noise and Student's-t noise
- …