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 $L_2$-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