193,019 research outputs found
Adaptive Higher-order Spectral Estimators
Many applications involve estimation of a signal matrix from a noisy data
matrix. In such cases, it has been observed that estimators that shrink or
truncate the singular values of the data matrix perform well when the signal
matrix has approximately low rank. In this article, we generalize this approach
to the estimation of a tensor of parameters from noisy tensor data. We develop
new classes of estimators that shrink or threshold the mode-specific singular
values from the higher-order singular value decomposition. These classes of
estimators are indexed by tuning parameters, which we adaptively choose from
the data by minimizing Stein's unbiased risk estimate. In particular, this
procedure provides a way to estimate the multilinear rank of the underlying
signal tensor. Using simulation studies under a variety of conditions, we show
that our estimators perform well when the mean tensor has approximately low
multilinear rank, and perform competitively when the signal tensor does not
have approximately low multilinear rank. We illustrate the use of these methods
in an application to multivariate relational data.Comment: 29 pages, 3 figure
Bayesian dimensionality reduction with PCA using penalized semi-integrated likelihood
We discuss the problem of estimating the number of principal components in
Principal Com- ponents Analysis (PCA). Despite of the importance of the problem
and the multitude of solutions proposed in the literature, it comes as a
surprise that there does not exist a coherent asymptotic framework which would
justify different approaches depending on the actual size of the data set. In
this paper we address this issue by presenting an approximate Bayesian approach
based on Laplace approximation and introducing a general method for building
the model selection criteria, called PEnalized SEmi-integrated Likelihood
(PESEL). Our general framework encompasses a variety of existing approaches
based on probabilistic models, like e.g. Bayesian Information Criterion for the
Probabilistic PCA (PPCA), and allows for construction of new criteria,
depending on the size of the data set at hand. Specifically, we define PESEL
when the number of variables substantially exceeds the number of observations.
We also report results of extensive simulation studies and real data analysis,
which illustrate good properties of our proposed criteria as compared to the
state-of- the-art methods and very recent proposals. Specifially, these
simulations show that PESEL based criteria can be quite robust against
deviations from the probabilistic model assumptions. Selected PESEL based
criteria for the estimation of the number of principal components are
implemented in R package varclust, which is available on github
(https://github.com/psobczyk/varclust).Comment: 31 pages, 7 figure
The Effect of Walkthrough Observations on Teacher Perspectives in Christian Schools
This study investigated the effects on teacher perceptions of frequent, brief classroom observations in Christian schools. Teachers (N=111) responded to 13 belief and value statements prior to and after the term during which administrators conducted weekly, brief, unannounced observations in their classes. Teachers reported significant positive change regarding (a) analyzing reasons for selecting methods to assess learning, (b) being encouraged after class observations, and (c) being encouraged after receiving feedback related to the observations
Effect of Applied Orthorhombic Lattice Distortion on the Antiferromagnetic Phase of CeAuSb
We study the response of the antiferromagnetism of CeAuSb to orthorhombic
lattice distortion applied through in-plane uniaxial pressure. The response to
pressure applied along a lattice direction shows a
first-order transition at zero pressure, which shows that the magnetic order
lifts the symmetry of the unstressed lattice. Sufficient
pressure appears to rotate the principal axes of the
order from to . At low pressure, the transition at is weakly first-order, however it
becomes continuous above a threshold pressure. We discuss
the possibility that this behavior is driven by order parameter fluctuations,
with the restoration of a continuous transition a result of reducing the
point-group symmetry of the lattice.Comment: 6 pages, 7 figure
Panel Data Tests Of PPP: A Critical Overview
This paper reviews recent developments in the analysis of non-stationary panels, focusing on empirical applications of panel unit root and cointegration tests in the context of PPP. It highlights various drawbacks of existing methods. First, unit root tests suffer from severe size distortions in the presence of negative moving average errors. Second, the common demeaning procedure to correct for the bias resulting from homogeneous cross-sectional dependence is not effective; more worryingly, it introduces cross-correlation when it is not already present. Third, standard corrections for the case of heterogeneous cross-sectional dependence do not generally produce consistent estimators. Fourth, if there is between-group correlation in the innovations, the SURE estimator is affected by similar problems to FGLS methods, and does not necessarily outperform OLS. Finally, cointegration between different groups in the panel could also be a source of size distortions. We offer some empirical guidelines to deal with these problems, but conclude that panel methods are unlikely to solve the PPP puzzl
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