116,685 research outputs found
Semiparametric estimation of spectral density function for irregular spatial data
Estimation of the covariance structure of spatial processes is of fundamental
importance in spatial statistics. In the literature, several non-parametric and
semi-parametric methods have been developed to estimate the covariance
structure based on the spectral representation of covariance functions.
However,they either ignore the high frequency properties of the spectral
density, which are essential to determine the performance of interpolation
procedures such as Kriging, or lack of theoretical justification. We propose a
new semi-parametric method to estimate spectral densities of isotropic spatial
processes with irregular observations. The spectral density function at low
frequencies is estimated using smoothing spline, while a parametric model is
used for the spectral density at high frequencies, and the parameters are
estimated by a method-of-moment approach based on empirical variograms at small
lags. We derive the asymptotic bounds for bias and variance of the proposed
estimator. The simulation study shows that our method outperforms the existing
non-parametric estimator by several performance criteria.Comment: 29 pages, 2 figure
A Euclidean likelihood estimator for bivariate tail dependence
The spectral measure plays a key role in the statistical modeling of
multivariate extremes. Estimation of the spectral measure is a complex issue,
given the need to obey a certain moment condition. We propose a Euclidean
likelihood-based estimator for the spectral measure which is simple and
explicitly defined, with its expression being free of Lagrange multipliers. Our
estimator is shown to have the same limit distribution as the maximum empirical
likelihood estimator of J. H. J. Einmahl and J. Segers, Annals of Statistics
37(5B), 2953--2989 (2009). Numerical experiments suggest an overall good
performance and identical behavior to the maximum empirical likelihood
estimator. We illustrate the method in an extreme temperature data analysis.Comment: 18 pages, 8 figure
Spectral Representation Learning for Conditional Moment Models
Many problems in causal inference and economics can be formulated in the
framework of conditional moment models, which characterize the target function
through a collection of conditional moment restrictions. For nonparametric
conditional moment models, efficient estimation often relies on preimposed
conditions on various measures of ill-posedness of the hypothesis space, which
are hard to validate when flexible models are used. In this work, we address
this issue by proposing a procedure that automatically learns representations
with controlled measures of ill-posedness. Our method approximates a linear
representation defined by the spectral decomposition of a conditional
expectation operator, which can be used for kernelized estimators and is known
to facilitate minimax optimal estimation in certain settings. We show this
representation can be efficiently estimated from data, and establish L2
consistency for the resulting estimator. We evaluate the proposed method on
proximal causal inference tasks, exhibiting promising performance on
high-dimensional, semi-synthetic data
Estimating stellar oscillation-related parameters and their uncertainties with the moment method
The moment method is a well known mode identification technique in
asteroseismology (where `mode' is to be understood in an astronomical rather
than in a statistical sense), which uses a time series of the first 3 moments
of a spectral line to estimate the discrete oscillation mode parameters l and
m. The method, contrary to many other mode identification techniques, also
provides estimates of other important continuous parameters such as the
inclination angle alpha, and the rotational velocity v_e. We developed a
statistical formalism for the moment method based on so-called generalized
estimating equations (GEE). This formalism allows the estimation of the
uncertainty of the continuous parameters taking into account that the different
moments of a line profile are correlated and that the uncertainty of the
observed moments also depends on the model parameters. Furthermore, we set up a
procedure to take into account the mode uncertainty, i.e., the fact that often
several modes (l,m) can adequately describe the data. We also introduce a new
lack of fit function which works at least as well as a previous discriminant
function, and which in addition allows us to identify the sign of the azimuthal
order m. We applied our method to the star HD181558, using several numerical
methods, from which we learned that numerically solving the estimating
equations is an intensive task. We report on the numerical results, from which
we gain insight in the statistical uncertainties of the physical parameters
involved in the moment method.Comment: The electronic online version from the publisher can be found at
http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9876.2005.00487.
A local moments estimation of the spectrum of a large dimensional covariance matrix
This paper considers the problem of estimating the population spectral distribution from a sample covariance matrix when its dimension is large. We generalize the contour-integral based method in Mestre (2008) and present a local moment estimation procedure. Compared with the original, the new procedure can be applied successfully to models where the asymptotic clusters of sample eigenvalues generated by different population eigenvalues are not all separate. The proposed estimates are proved to be consistent. Numerical results illustrate the implementation of the estimation procedure and demonstrate its efficiency in various cases.postprin
The modified Yule-Walker method for multidimensional infinite-variance periodic autoregressive model of order 1
The time series with periodic behavior, such as the periodic autoregressive
(PAR) models belonging to the class of the periodically correlated processes,
are present in various real applications. In the literature, such processes
were considered in different directions, especially with the
Gaussian-distributed noise. However, in most of the applications, the
assumption of the finite-variance distribution seems to be too simplified.
Thus, one can consider the extensions of the classical PAR model where the
non-Gaussian distribution is applied. In particular, the Gaussian distribution
can be replaced by the infinite-variance distribution, e.g. by the
stable distribution. In this paper, we focus on the multidimensional
stable PAR time series models. For such models, we propose a new
estimation method based on the Yule-Walker equations. However, since for the
infinite-variance case the covariance does not exist, thus it is replaced by
another measure, namely the covariation. In this paper we propose to apply two
estimators of the covariation measure. The first one is based on moment
representation (moment-based) while the second one - on the spectral measure
representation (spectral-based). The validity of the new approaches are
verified using the Monte Carlo simulations in different contexts, including the
sample size and the index of stability of the noise. Moreover, we compare the
moment-based covariation-based method with spectral-based covariation-based
technique. Finally, the real data analysis is presented.Comment: 31 pages, 17 figure
The experimental determination of tyre model parameters
SUMMARY
This report describes the analysis of a series of experiments on pneumatic tyres
which were designed to test the various hypotheses: regarding the deformed shape of a
tyre during the steering process.
The experiments consisted of several separate tests first described in Ref. 1 and 2.
a) The application of a point lateral force or a moment at one position on the tread band
which is restrained at the centre of the wheel, and the measurement of the resulting
lateral deflection of each point of the tyre perimeter.
b) The application of a uniform force around the tyre perimeter on a hollow cylindrical
former and applying a load at the centre of the wheel.
c) Direct determination of tread band tension by cutting the tread band and bridging the
cut by a dynamometer.
d) Estimation of the bending modulus of the tread band by test on sections cut from the
tread band.
The analysis of the experiments is carried out by first transforming the test results
into a Fourier series and determining the spectral content of the bending line with an
harmonic analysis. Transfer functions of beam and string models are derived and applied
to the test results. A method of considering a three parameter model is described
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