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We study the limit law of a vector made up of normalized sums of functions of long-range dependent stationary Gaussian series. Depending on the memory parameter of the Gaussian series and on the Hermite ranks of the functions, the resulting limit law may be (a) a multi-variate Gaussian process involving dependent Brownian motion marginals, (b) a multi-variate process involving dependent Hermite processes as marginals or (c) a combination. We treat cases (a) and (b) in general and case (c) when the Hermite components involve ranks 1 and 2. We include a conjecture about case (c) when the Hermite ranks are arbitrary, although the conjecture can be resolved in some special cases. [ABSTRACT FROM AUTHOR]

This article extends the self‐normalized subsampling method of Bai et al. (2016) to the M‐estimation of linear regression models, where the covariate and the noise are stationary time series which may have long‐range dependence or heavy tails. The method yields an asymptotic confidence region for the unknown coefficients of the linear regression. The determination of these regions does not involve unknown parameters such as the intensity of the dependence or the heaviness of the distributional tail of the time series. Additional simulations can be found in a supplement. The computer codes are available from the authors. [ABSTRACT FROM AUTHOR]

We report luminous polylactic acid (PLA) composite prepared via a solvent casting method using different amounts of phosphor strontium aluminate (SrAl 2 O 4 : Eu 2+ and Dy 3+ ) (SAO). The reason for doing this is that the changes of fluorescence and mechanical properties in the composites with different SAO contents can be directly evaluated. The SAO particles should have a variety of excellent characteristics in the PLA matrix, among which dispersibility and compatibility are particularly important; so, they can be modified by 3-aminopropyltriethoxysilane (APS) to achieve the target characteristics. The results showed that the fluorescence and mechanical properties were affected by SAO addition. The mechanical properties significantly improved with 5 wt% SAO; further, addition had no impact. And the emission band of fluorescence and phosphorescence is just at the peak of 524 nm. The composites with 15 wt% SAO have the best fluorescence properties. The fluorescence decreased with further doping. Fluorescence decay curves with various amounts of SAO particles show a similar tendency as pure SAO particles; the speed of decrease in afterglow intensity was higher for the first 30 min. In addition, the detailed morphological scanning and study by scanning electron microscope (SEM) showed that the particles had good adhesion to the matrix. In conclusion, the concentration of SAO into the PLA matrix impacts the fluorescence and mechanical properties of a SAO/PLA composite material., Competing Interests: It is declared by the authors that this article is free of conflict of interest., (Copyright © 2021 Zhongjin Ni et al.)

Estimating the dependence structure of multidimensional time series data in real-time is challenging. With large volumes of streaming data, the problem becomes more difficult when the multidimensional data are collected asynchronously across distributed nodes, which motivates us to sample representative data points from streams. We propose a leverage score sampling (LSS) method for efficient online inference of the streaming vector autoregressive (VAR) model. We define the leverage score for the streaming VAR model so that the LSS method selects informative data points in real-time with statistical guarantees of parameter estimation efficiency. Moreover, our LSS method can be directly deployed in an asynchronous decentralized environment, e.g., a sensor network without a fusion center, and produce asynchronous consensus online parameter estimation over time. By exploiting the temporal dependence structure of the VAR model, the LSS method selects samples independently on each dimension and thus is able to update the estimation asynchronously. We illustrate the effectiveness of the LSS method in synthetic, gas sensor and seismic datasets.