2,872 research outputs found
On the least squares estimator in a nearly unstable sequence of stationary spatial AR models
A nearly unstable sequence of stationary spatial autoregressive processes is
investigated, when the sum of the absolute values of the autoregressive
coefficients tends to one. It is shown that after an appropriate norming the
least squares estimator for these coefficients has a normal limit distribution.
If none of the parameters equals zero than the typical rate of convergence is
n.Comment: 26 pages To appear in: J. Multivariate Ana
Covariance Estimation: The GLM and Regularization Perspectives
Finding an unconstrained and statistically interpretable reparameterization
of a covariance matrix is still an open problem in statistics. Its solution is
of central importance in covariance estimation, particularly in the recent
high-dimensional data environment where enforcing the positive-definiteness
constraint could be computationally expensive. We provide a survey of the
progress made in modeling covariance matrices from two relatively complementary
perspectives: (1) generalized linear models (GLM) or parsimony and use of
covariates in low dimensions, and (2) regularization or sparsity for
high-dimensional data. An emerging, unifying and powerful trend in both
perspectives is that of reducing a covariance estimation problem to that of
estimating a sequence of regression problems. We point out several instances of
the regression-based formulation. A notable case is in sparse estimation of a
precision matrix or a Gaussian graphical model leading to the fast graphical
LASSO algorithm. Some advantages and limitations of the regression-based
Cholesky decomposition relative to the classical spectral (eigenvalue) and
variance-correlation decompositions are highlighted. The former provides an
unconstrained and statistically interpretable reparameterization, and
guarantees the positive-definiteness of the estimated covariance matrix. It
reduces the unintuitive task of covariance estimation to that of modeling a
sequence of regressions at the cost of imposing an a priori order among the
variables. Elementwise regularization of the sample covariance matrix such as
banding, tapering and thresholding has desirable asymptotic properties and the
sparse estimated covariance matrix is positive definite with probability
tending to one for large samples and dimensions.Comment: Published in at http://dx.doi.org/10.1214/11-STS358 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Variational Data Assimilation via Sparse Regularization
This paper studies the role of sparse regularization in a properly chosen
basis for variational data assimilation (VDA) problems. Specifically, it
focuses on data assimilation of noisy and down-sampled observations while the
state variable of interest exhibits sparsity in the real or transformed domain.
We show that in the presence of sparsity, the -norm regularization
produces more accurate and stable solutions than the classic data assimilation
methods. To motivate further developments of the proposed methodology,
assimilation experiments are conducted in the wavelet and spectral domain using
the linear advection-diffusion equation
A selective overview of nonparametric methods in financial econometrics
This paper gives a brief overview on the nonparametric techniques that are
useful for financial econometric problems. The problems include estimation and
inferences of instantaneous returns and volatility functions of
time-homogeneous and time-dependent diffusion processes, and estimation of
transition densities and state price densities. We first briefly describe the
problems and then outline main techniques and main results. Some useful
probabilistic aspects of diffusion processes are also briefly summarized to
facilitate our presentation and applications.Comment: 32 pages include 7 figure
Bootstrap methods applied to spatial variogram estimation and sequential sampling
The topics, estimation of spatial variogram, bootstrap method for stationary processes and sequential sampling are studied in this thesis. Condition and exact covariance formulars are derived for Matheron\u27s variogram estimators. The asymptotic properties of the least square estimator of the spatial variogram are also shown. Block bootstrap method is applied to get more efficient generalized least square estimator. Consistency and the asymptotic normality of the bootstrap based generalized least square estimators are proved. Performances of the least square estimators with finite sample are compared by simulation study which uses the random field generated by spectral method. Bias due to the repeated significance test which is an advanced version of sequential probability ratio test is estimated by bootstrap method
A specification test for nonlinear nonstationary models
We provide a limit theory for a general class of kernel smoothed U-statistics
that may be used for specification testing in time series regression with
nonstationary data. The test framework allows for linear and nonlinear models
with endogenous regressors that have autoregressive unit roots or near unit
roots. The limit theory for the specification test depends on the
self-intersection local time of a Gaussian process. A new weak convergence
result is developed for certain partial sums of functions involving
nonstationary time series that converges to the intersection local time
process. This result is of independent interest and is useful in other
applications. Simulations examine the finite sample performance of the test.Comment: Published in at http://dx.doi.org/10.1214/12-AOS975 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Parameter estimation in a spatial unit root autoregressive model
Spatial unilateral autoregressive model is investigated in the
unit root case, that is when the parameters are on the boundary of the domain
of stability that forms a tetrahedron with vertices $(1,1,-1), \ (1,-1,1),\
(-1,1,1)(-1,-1,-1)nn^{3/2}$.Comment: 47 pages, 1 figur
Optimal Estimation Methodologies for Panel Data Regression Models
This survey study discusses main aspects to optimal estimation methodologies
for panel data regression models. In particular, we present current
methodological developments for modeling stationary panel data as well as
robust methods for estimation and inference in nonstationary panel data
regression models. Some applications from the network econometrics and high
dimensional statistics literature are also discussed within a stationary time
series environment
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