2,339 research outputs found
Marginal empirical likelihood and sure independence feature screening
We study a marginal empirical likelihood approach in scenarios when the
number of variables grows exponentially with the sample size. The marginal
empirical likelihood ratios as functions of the parameters of interest are
systematically examined, and we find that the marginal empirical likelihood
ratio evaluated at zero can be used to differentiate whether an explanatory
variable is contributing to a response variable or not. Based on this finding,
we propose a unified feature screening procedure for linear models and the
generalized linear models. Different from most existing feature screening
approaches that rely on the magnitudes of some marginal estimators to identify
true signals, the proposed screening approach is capable of further
incorporating the level of uncertainties of such estimators. Such a merit
inherits the self-studentization property of the empirical likelihood approach,
and extends the insights of existing feature screening methods. Moreover, we
show that our screening approach is less restrictive to distributional
assumptions, and can be conveniently adapted to be applied in a broad range of
scenarios such as models specified using general moment conditions. Our
theoretical results and extensive numerical examples by simulations and data
analysis demonstrate the merits of the marginal empirical likelihood approach.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1139 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A test for model specification of diffusion processes
We propose a test for model specification of a parametric diffusion process
based on a kernel estimation of the transitional density of the process. The
empirical likelihood is used to formulate a statistic, for each kernel
smoothing bandwidth, which is effectively a Studentized -distance between
the kernel transitional density estimator and the parametric transitional
density implied by the parametric process. To reduce the sensitivity of the
test on smoothing bandwidth choice, the final test statistic is constructed by
combining the empirical likelihood statistics over a set of smoothing
bandwidths. To better capture the finite sample distribution of the test
statistic and data dependence, the critical value of the test is obtained by a
parametric bootstrap procedure. Properties of the test are evaluated
asymptotically and numerically by simulation and by a real data example.Comment: Published in at http://dx.doi.org/10.1214/009053607000000659 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Optimal covariance matrix estimation for high-dimensional noise in high-frequency data
In this paper, we consider efficiently learning the structural information
from the highdimensional noise in high-frequency data via estimating its
covariance matrix with optimality. The problem is uniquely challenging due to
the latency of the targeted high-dimensional vector containing the noises, and
the practical reality that the observed data can be highly asynchronous -- not
all components of the high-dimensional vector are observed at the same time
points. To meet the challenges, we propose a new covariance matrix estimator
with appropriate localization and thresholding. In the setting with latency and
asynchronous observations, we establish the minimax optimal convergence rates
associated with two commonly used loss functions for the covariance matrix
estimations. As a major theoretical development, we show that despite the
latency of the signal in the high-frequency data, the optimal rates remain the
same as if the targeted high-dimensional noises are directly observable. Our
results indicate that the optimal rates reflect the impact due to the
asynchronous observations, which are slower than that with synchronous
observations. Furthermore, we demonstrate that the proposed localized estimator
with thresholding achieves the minimax optimal convergence rates. We also
illustrate the empirical performance of the proposed estimator with extensive
simulation studies and a real data analysis
Status epilepticus alters hippocampal PKAβ and PKAγ expression in mice
AbstractObjectivesTo investigate the localization and progressive changes of cyclic-AMP dependent protein kinase (cPKA) in the mouse hippocampus at acute stages during and after pilocarpine induced status epilepticus.MethodsPilocarpine induced status epilepticus mice were sacrificed 30min, 2h or 1 day after the start of a ∼7h lasting status as assessed by video-electroencephalography. Brains were processed for quantitative immunohistochemistry of hippocampal cPKAβ and cPKAγ, and immunohistochemical co-localization of cPKAβ and cPKAγ with calbindin (CB), calretinin (CR), and parvalbumin (PV).ResultsBased on anatomical and morphological assessment, cPKAβ was primarily expressed by principal cells and cPKAγ by interneurons. In CA1, cPKAβ co-localized with 76% of CB, 41% of CR, and 95% of PV-immunopositive cells, while cPKAγ co-localized with 50% of CB, 29% of CR, and 80% of PV-immunopositive cells. Upon induction of status epilepticus, cPKAβ expression was transiently reduced in CA1, whereas cPKAγ expression was sustainably reduced.ConclusioncPKA may play an important role in neuronal hyperexcitability, death and epileptogenesis during and after pilocarpine induced status epilepticus
Parameters Estimation and Bias Correction for Diffusion Processes
This paper considers parameter estimation for continuous-time diffusion processes which are commonly used to model dynamics of financial securities including interest rates. To understand why the drift parameters are more difficult to estimate than the diffusion parameter as observed in many empirical studies, we develop expansions for the bias and variance of parameter estimators for two mostly employed interest rate processes. A parametric bootstrap procedure is proposed to correct bias in parameter estimation of general diffusion processes. Simulation studies confirm the theoretical findings and show that the bootstrap proposal can effectively reduce both the bias and the mean square error of parameter estimates for both univariate and multivariate processes. The advantages of using more accurate parameter estimators when calculating various option prices in finance are demonstrated by an empirical study on a Fed fund rate data
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