44,999 research outputs found
Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap
This paper investigates the use of bootstrap-based bias correction of
semi-parametric estimators of the long memory parameter in fractionally
integrated processes. The re-sampling method involves the application of the
sieve bootstrap to data pre-filtered by a preliminary semi-parametric estimate
of the long memory parameter. Theoretical justification for using the bootstrap
techniques to bias adjust log-periodogram and semi-parametric local Whittle
estimators of the memory parameter is provided. Simulation evidence comparing
the performance of the bootstrap bias correction with analytical bias
correction techniques is also presented. The bootstrap method is shown to
produce notable bias reductions, in particular when applied to an estimator for
which analytical adjustments have already been used. The empirical coverage of
confidence intervals based on the bias-adjusted estimators is very close to the
nominal, for a reasonably large sample size, more so than for the comparable
analytically adjusted estimators. The precision of inferences (as measured by
interval length) is also greater when the bootstrap is used to bias correct
rather than analytical adjustments.Comment: 38 page
Stochastic Behavior Analysis of the Gaussian Kernel Least-Mean-Square Algorithm
The kernel least-mean-square (KLMS) algorithm is a popular algorithm in nonlinear adaptive filtering due to its
simplicity and robustness. In kernel adaptive filters, the statistics of the input to the linear filter depends on the parameters of the kernel employed. Moreover, practical implementations require a finite nonlinearity model order. A Gaussian KLMS has two design parameters, the step size and the Gaussian kernel bandwidth. Thus, its design requires analytical models for the algorithm behavior as a function of these two parameters. This paper studies the steady-state behavior and the transient behavior of the
Gaussian KLMS algorithm for Gaussian inputs and a finite order nonlinearity model. In particular, we derive recursive expressions for the mean-weight-error vector and the mean-square-error. The model predictions show excellent agreement with Monte Carlo simulations in transient and steady state. This allows the explicit analytical determination of stability limits, and gives opportunity
to choose the algorithm parameters a priori in order to achieve prescribed convergence speed and quality of the estimate. Design examples are presented which validate the theoretical analysis and illustrates its application
Single camera pose estimation using Bayesian filtering and Kinect motion priors
Traditional approaches to upper body pose estimation using monocular vision
rely on complex body models and a large variety of geometric constraints. We
argue that this is not ideal and somewhat inelegant as it results in large
processing burdens, and instead attempt to incorporate these constraints
through priors obtained directly from training data. A prior distribution
covering the probability of a human pose occurring is used to incorporate
likely human poses. This distribution is obtained offline, by fitting a
Gaussian mixture model to a large dataset of recorded human body poses, tracked
using a Kinect sensor. We combine this prior information with a random walk
transition model to obtain an upper body model, suitable for use within a
recursive Bayesian filtering framework. Our model can be viewed as a mixture of
discrete Ornstein-Uhlenbeck processes, in that states behave as random walks,
but drift towards a set of typically observed poses. This model is combined
with measurements of the human head and hand positions, using recursive
Bayesian estimation to incorporate temporal information. Measurements are
obtained using face detection and a simple skin colour hand detector, trained
using the detected face. The suggested model is designed with analytical
tractability in mind and we show that the pose tracking can be
Rao-Blackwellised using the mixture Kalman filter, allowing for computational
efficiency while still incorporating bio-mechanical properties of the upper
body. In addition, the use of the proposed upper body model allows reliable
three-dimensional pose estimates to be obtained indirectly for a number of
joints that are often difficult to detect using traditional object recognition
strategies. Comparisons with Kinect sensor results and the state of the art in
2D pose estimation highlight the efficacy of the proposed approach.Comment: 25 pages, Technical report, related to Burke and Lasenby, AMDO 2014
conference paper. Code sample: https://github.com/mgb45/SignerBodyPose Video:
https://www.youtube.com/watch?v=dJMTSo7-uF
Higher-Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes
This paper investigates the accuracy of bootstrap-based inference in the case
of long memory fractionally integrated processes. The re-sampling method is
based on the semi-parametric sieve approach, whereby the dynamics in the
process used to produce the bootstrap draws are captured by an autoregressive
approximation. Application of the sieve method to data pre-filtered by a
semi-parametric estimate of the long memory parameter is also explored.
Higher-order improvements yielded by both forms of re-sampling are demonstrated
using Edgeworth expansions for a broad class of statistics that includes first-
and second-order moments, the discrete Fourier transform and regression
coefficients. The methods are then applied to the problem of estimating the
sampling distributions of the sample mean and of selected sample
autocorrelation coefficients, in experimental settings. In the case of the
sample mean, the pre-filtered version of the bootstrap is shown to avoid the
distinct underestimation of the sampling variance of the mean which the raw
sieve method demonstrates in finite samples, higher order accuracy of the
latter notwithstanding. Pre-filtering also produces gains in terms of the
accuracy with which the sampling distributions of the sample autocorrelations
are reproduced, most notably in the part of the parameter space in which
asymptotic normality does not obtain. Most importantly, the sieve bootstrap is
shown to reproduce the (empirically infeasible) Edgeworth expansion of the
sampling distribution of the autocorrelation coefficients, in the part of the
parameter space in which the expansion is valid
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