119 research outputs found
Regularized Nonparametric Volterra Kernel Estimation
In this paper, the regularization approach introduced recently for
nonparametric estimation of linear systems is extended to the estimation of
nonlinear systems modelled as Volterra series. The kernels of order higher than
one, representing higher dimensional impulse responses in the series, are
considered to be realizations of multidimensional Gaussian processes. Based on
this, prior information about the structure of the Volterra kernel is
introduced via an appropriate penalization term in the least squares cost
function. It is shown that the proposed method is able to deliver accurate
estimates of the Volterra kernels even in the case of a small amount of data
points
Laplace deconvolution with noisy observations
In the present paper we consider Laplace deconvolution for discrete noisy
data observed on the interval whose length may increase with a sample size.
Although this problem arises in a variety of applications, to the best of our
knowledge, it has been given very little attention by the statistical
community. Our objective is to fill this gap and provide statistical treatment
of Laplace deconvolution problem with noisy discrete data. The main
contribution of the paper is explicit construction of an asymptotically
rate-optimal (in the minimax sense) Laplace deconvolution estimator which is
adaptive to the regularity of the unknown function. We show that the original
Laplace deconvolution problem can be reduced to nonparametric estimation of a
regression function and its derivatives on the interval of growing length T_n.
Whereas the forms of the estimators remain standard, the choices of the
parameters and the minimax convergence rates, which are expressed in terms of
T_n^2/n in this case, are affected by the asymptotic growth of the length of
the interval.
We derive an adaptive kernel estimator of the function of interest, and
establish its asymptotic minimaxity over a range of Sobolev classes. We
illustrate the theory by examples of construction of explicit expressions of
Laplace deconvolution estimators. A simulation study shows that, in addition to
providing asymptotic optimality as the number of observations turns to
infinity, the proposed estimator demonstrates good performance in finite sample
examples
Laplace deconvolution and its application to Dynamic Contrast Enhanced imaging
In the present paper we consider the problem of Laplace deconvolution with
noisy discrete observations. The study is motivated by Dynamic Contrast
Enhanced imaging using a bolus of contrast agent, a procedure which allows
considerable improvement in {evaluating} the quality of a vascular network and
its permeability and is widely used in medical assessment of brain flows or
cancerous tumors. Although the study is motivated by medical imaging
application, we obtain a solution of a general problem of Laplace deconvolution
based on noisy data which appears in many different contexts. We propose a new
method for Laplace deconvolution which is based on expansions of the
convolution kernel, the unknown function and the observed signal over Laguerre
functions basis. The expansion results in a small system of linear equations
with the matrix of the system being triangular and Toeplitz. The number of
the terms in the expansion of the estimator is controlled via complexity
penalty. The advantage of this methodology is that it leads to very fast
computations, does not require exact knowledge of the kernel and produces no
boundary effects due to extension at zero and cut-off at . The technique
leads to an estimator with the risk within a logarithmic factor of of the
oracle risk under no assumptions on the model and within a constant factor of
the oracle risk under mild assumptions. The methodology is illustrated by a
finite sample simulation study which includes an example of the kernel obtained
in the real life DCE experiments. Simulations confirm that the proposed
technique is fast, efficient, accurate, usable from a practical point of view
and competitive
Stage-discharge relationship in tidal channels
Author Posting. © The Author(s), 2016. This is the author's version of the work. It is posted here by permission of Association for the Sciences of Limnology and Oceanography for personal use, not for redistribution. The definitive version was published in Limnology and Oceanography: Methods 15 (2017): 394–407, doi:10.1002/lom3.10168.Long-term records of the flow of water through tidal channels are essential to constrain
the budgets of sediments and biogeochemical compounds in salt marshes. Statistical
models which relate discharge to water level allow the estimation of such records from
more easily obtained records of water stage in the channel. Here we compare four
different types of stage-discharge models, each of which captures different characteristics
of the stage-discharge relationship. We estimate and validate each of these models on a
two-month long time series of stage and discharge obtained with an Acoustic Doppler
Current Profiler in a salt marsh channel. We find that the best performance is obtained by
models that account for the nonlinear and time-varying nature of the stage-discharge
relationship. Good performance can also be obtained from a simplified version of these
models, which captures nonlinearity and nonstationarity without the complexity of the
fully nonlinear or time-varying models.This research was supported by the National Science Foundation (awards OCE1354251,
OCE1354494, and OCE1238212).2018-04-2
An Offline Learning Approach to Propagator Models
We consider an offline learning problem for an agent who first estimates an
unknown price impact kernel from a static dataset, and then designs strategies
to liquidate a risky asset while creating transient price impact. We propose a
novel approach for a nonparametric estimation of the propagator from a dataset
containing correlated price trajectories, trading signals and metaorders. We
quantify the accuracy of the estimated propagator using a metric which depends
explicitly on the dataset. We show that a trader who tries to minimise her
execution costs by using a greedy strategy purely based on the estimated
propagator will encounter suboptimality due to so-called spurious correlation
between the trading strategy and the estimator and due to intrinsic uncertainty
resulting from a biased cost functional. By adopting an offline reinforcement
learning approach, we introduce a pessimistic loss functional taking the
uncertainty of the estimated propagator into account, with an optimiser which
eliminates the spurious correlation, and derive an asymptotically optimal bound
on the execution costs even without precise information on the true propagator.
Numerical experiments are included to demonstrate the effectiveness of the
proposed propagator estimator and the pessimistic trading strategy.Comment: 12 figure
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