25,527 research outputs found
Partial Least Squares for Serially Dependent Data
In the first paper we consider the partial least squares algorithm for dependent data and study the consequences
of ignoring the dependence both theoretically and numerically. Ignoring nonstationary dependence
structures can lead to inconsistent estimation, but a simple modification leads to consistent
estimation. A protein dynamics example illustrates the superior predictive power of the
method. For the second paper we consider the kernel partial least squares algorithm for the solution of nonparametric regression
problems when the data exhibit dependence in their observations in the form of stationary
time series. Probabilistic convergence rates of the kernel partial least squares estimator to the
true regression function are established under a source condition. The impact of long range
dependence in the data is studied both theoretically and in simulations
Estimation in semi-parametric regression with non-stationary regressors
In this paper, we consider a partially linear model of the form
, , where is a
null recurrent Markov chain, is a sequence of either strictly
stationary or non-stationary regressors and is a stationary
sequence. We propose to estimate both and by a
semi-parametric least-squares (SLS) estimation method. Under certain
conditions, we then show that the proposed SLS estimator of is still
asymptotically normal with the same rate as for the case of stationary time
series. In addition, we also establish an asymptotic distribution for the
nonparametric estimator of the function . Some numerical examples are
provided to show that our theory and estimation method work well in practice.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ344 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Analytic Properties and Covariance Functions of a New Class of Generalized Gibbs Random Fields
Spartan Spatial Random Fields (SSRFs) are generalized Gibbs random fields,
equipped with a coarse-graining kernel that acts as a low-pass filter for the
fluctuations. SSRFs are defined by means of physically motivated spatial
interactions and a small set of free parameters (interaction couplings). This
paper focuses on the FGC-SSRF model, which is defined on the Euclidean space
by means of interactions proportional to the squares of the
field realizations, as well as their gradient and curvature. The permissibility
criteria of FGC-SSRFs are extended by considering the impact of a
finite-bandwidth kernel. It is proved that the FGC-SSRFs are almost surely
differentiable in the case of finite bandwidth. Asymptotic explicit expressions
for the Spartan covariance function are derived for and ; both known
and new covariance functions are obtained depending on the value of the
FGC-SSRF shape parameter. Nonlinear dependence of the covariance integral scale
on the FGC-SSRF characteristic length is established, and it is shown that the
relation becomes linear asymptotically. The results presented in this paper are
useful in random field parameter inference, as well as in spatial interpolation
of irregularly-spaced samples.Comment: 24 pages; 4 figures Submitted for publication to IEEE Transactions on
Information Theor
TESTING THE HYPOTHESIS OF AN EFFICIENT MARKET IN TERMS OF INFORMATION – THE CASE OF THE CAPITAL MARKET IN ROMANIA DURING RECESSION
This paper is trying to test the hypothesis of efficient market (EMH Efficient Market Hypothesis), the case of capital market in Romania during the economic financial crisis. According to the purpose in view our research is aiming at testing the hypothesis of random walk of stock exchange indexes BET, BET-C, BET_FI of Bucharest Stock Exchange. In this respect we will enforce statistic tests to see if the capital market in Romania is efficient in a weak form during this period.efficient capital market, random walk, stationary tests, normal distribution
The generalized shrinkage estimator for the analysis of functional connectivity of brain signals
We develop a new statistical method for estimating functional connectivity
between neurophysiological signals represented by a multivariate time series.
We use partial coherence as the measure of functional connectivity. Partial
coherence identifies the frequency bands that drive the direct linear
association between any pair of channels. To estimate partial coherence, one
would first need an estimate of the spectral density matrix of the multivariate
time series. Parametric estimators of the spectral density matrix provide good
frequency resolution but could be sensitive when the parametric model is
misspecified. Smoothing-based nonparametric estimators are robust to model
misspecification and are consistent but may have poor frequency resolution. In
this work, we develop the generalized shrinkage estimator, which is a weighted
average of a parametric estimator and a nonparametric estimator. The optimal
weights are frequency-specific and derived under the quadratic risk criterion
so that the estimator, either the parametric estimator or the nonparametric
estimator, that performs better at a particular frequency receives heavier
weight. We validate the proposed estimator in a simulation study and apply it
on electroencephalogram recordings from a visual-motor experiment.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS396 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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