170 research outputs found
Re-calibration of sample means
We consider the problem of calibration and the GREG method as suggested and
studied in Deville and Sarndal (1992). We show that a GREG type estimator is
typically not minimal variance unbiased estimator even asymptotically. We
suggest a similar estimator which is unbiased but is asymptotically with a
minimal variance
Semiparametric curve alignment and shift density estimation for biological data
Assume that we observe a large number of curves, all of them with identical,
although unknown, shape, but with a different random shift. The objective is to
estimate the individual time shifts and their distribution. Such an objective
appears in several biological applications like neuroscience or ECG signal
processing, in which the estimation of the distribution of the elapsed time
between repetitive pulses with a possibly low signal-noise ratio, and without a
knowledge of the pulse shape is of interest. We suggest an M-estimator leading
to a three-stage algorithm: we split our data set in blocks, on which the
estimation of the shifts is done by minimizing a cost criterion based on a
functional of the periodogram; the estimated shifts are then plugged into a
standard density estimator. We show that under mild regularity assumptions the
density estimate converges weakly to the true shift distribution. The theory is
applied both to simulations and to alignment of real ECG signals. The estimator
of the shift distribution performs well, even in the case of low
signal-to-noise ratio, and is shown to outperform the standard methods for
curve alignment.Comment: 30 pages ; v5 : minor changes and correction in the proof of
Proposition 3.
Sparse regression algorithm for activity estimation in spectrometry
We consider the counting rate estimation of an unknown radioactive source,
which emits photons at times modeled by an homogeneous Poisson process. A
spectrometer converts the energy of incoming photons into electrical pulses,
whose number provides a rough estimate of the intensity of the Poisson process.
When the activity of the source is high, a physical phenomenon known as pileup
effect distorts direct measurements, resulting in a significant bias to the
standard estimators of the source activities used so far in the field. We show
in this paper that the problem of counting rate estimation can be interpreted
as a sparse regression problem. We suggest a post-processed, non-negative,
version of the Least Absolute Shrinkage and Selection Operator (LASSO) to
estimate the photon arrival times. The main difficulty in this problem is that
no theoretical conditions can guarantee consistency in sparsity of LASSO,
because the dictionary is not ideal and the signal is sampled. We therefore
derive theoretical conditions and bounds which illustrate that the proposed
method can none the less provide a good, close to the best attainable, estimate
of the counting rate activity. The good performances of the proposed approach
are studied on simulations and real datasets
The Bayesian Analysis of Complex, High-Dimensional Models: Can It Be CODA?
We consider the Bayesian analysis of a few complex, high-dimensional models
and show that intuitive priors, which are not tailored to the fine details of
the model and the estimated parameters, produce estimators which perform poorly
in situations in which good, simple frequentist estimators exist. The models we
consider are: stratified sampling, the partial linear model, linear and
quadratic functionals of white noise and estimation with stopping times. We
present a strong version of Doob's consistency theorem which demonstrates that
the existence of a uniformly -consistent estimator ensures that the
Bayes posterior is -consistent for values of the parameter in subsets
of prior probability 1. We also demonstrate that it is, at least, in principle,
possible to construct Bayes priors giving both global and local minimax rates,
using a suitable combination of loss functions. We argue that there is no
contradiction in these apparently conflicting findings.Comment: Published in at http://dx.doi.org/10.1214/14-STS483 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Semiparametric Curve Alignment and Shift Density Estimation: ECG Data Processing Revisited
We address in this contribution a problem stemming from functional data analysis. Assuming that we dispose of a large number of shifted recorded curves with identical shape, the objective is to estimate the time shifts as well as their distribution. Such an objective appears in several biological applications, for example in ECG signal processing. We are interested in the estimation of the distribution of elapsed durations between repetitive pulses, but wish to estimate it with a possibly low signal-to-noise ratio, or without any knowledge of the pulse shape. This problem is solved within a semiparametric framework, that is without any knowledge of the shape. We suggest an M-estimator leading to two different algorithms whose main steps are as follows: we split our dataset in blocks, on which the estimation of the shifts is done by minimizing a cost criterion, based on a functional of the periodogram. The estimated shifts are then plugged into a standard density estimator. Some theoretical insights are presented, which show that under mild assumptions the alignment can be done efficiently. Results are presented on simulations, as well as on real data for the alignment of ECG signals, and these algorithms are compared to the methods used by practitioners in this framework. It is shown in the results that the presented method outperforms the standard ones, thus leading to a more accurate estimation of the average heart pulse and of the distribution of elapsed times between heart pulses, even in the case of low Signal-to- Noise Ratio (SNR)
Data-driven efficient score tests for deconvolution problems
We consider testing statistical hypotheses about densities of signals in
deconvolution models. A new approach to this problem is proposed. We
constructed score tests for the deconvolution with the known noise density and
efficient score tests for the case of unknown density. The tests are
incorporated with model selection rules to choose reasonable model dimensions
automatically by the data. Consistency of the tests is proved
Semiparametric Multivariate Accelerated Failure Time Model with Generalized Estimating Equations
The semiparametric accelerated failure time model is not as widely used as
the Cox relative risk model mainly due to computational difficulties. Recent
developments in least squares estimation and induced smoothing estimating
equations provide promising tools to make the accelerate failure time models
more attractive in practice. For semiparametric multivariate accelerated
failure time models, we propose a generalized estimating equation approach to
account for the multivariate dependence through working correlation structures.
The marginal error distributions can be either identical as in sequential event
settings or different as in parallel event settings. Some regression
coefficients can be shared across margins as needed. The initial estimator is a
rank-based estimator with Gehan's weight, but obtained from an induced
smoothing approach with computation ease. The resulting estimator is consistent
and asymptotically normal, with a variance estimated through a multiplier
resampling method. In a simulation study, our estimator was up to three times
as efficient as the initial estimator, especially with stronger multivariate
dependence and heavier censoring percentage. Two real examples demonstrate the
utility of the proposed method
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