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In this paper, a stochastic optimization framework is proposed to address the microgrid energy dispatching problem with random renewable generation and vehicle activity pattern, which is closer to the practical applications. The patterns of energy generation, consumption and storage availability are all random and unknown at the beginning, and the microgrid controller design (MCD) is formulated as a Markov decision process (MDP). Hence, an online learning-based control algorithm is proposed for the microgrid, which could adapt the control policy with increasing knowledge of the system dynamics and converges to the optimal algorithm. We adopt the linear approximation idea to decompose the original value functions as the summation of each per-battery value function. As a consequence, the computational complexity is significantly reduced from exponential growth to linear growth with respect to the size of battery states. Monte Carlo simulation of different scenarios demonstrates the effectiveness and efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper we introduce a weighted composite quantile regression (CQR) estimation approach and study its application in nonlinear models such as exponential models and ARCH-type models. The weighted CQR is augmented by using a data-driven weighting scheme. With the error distribution unspecified, the proposed estimators share robustness from quantile regression and achieve nearly the same efficiency as the oracle maximum likelihood estimator (MLE) for a variety of error distributions including the normal, mixed-normal, Student’s t , Cauchy distributions, etc. We also suggest an algorithm for the fast implementation of the proposed methodology. Simulations are carried out to compare the performance of different estimators, and the proposed approach is used to analyze the daily S&P 500 Composite index, which verifies the effectiveness and efficiency of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we study spatial quantile regression estimation of multivariate threshold time series models. Bahadur’s representations for our estimators are established, which naturally lead to asymptotic normality of the estimators. Simulations and a real example are used to evaluate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

We propose a geoadditive model with spatial random effects to model the earthquake distribution in Mainland China. The error is modeled an infinite mixture of Gaussian distributions with a stochastic constraint that ensures inference on the quantiles of interest. The spatial random effects are used to capture individual area effects which allow for heterogeneity among regions. We run Bayesian quantile regression for the spatial trend of the geoadditive model under a flexible Bayesian framework. The proposed method not only allows for a full span of quantile-restricted error distributions, but also separates a large-scale geographical trend from local spatial correlation. This makes the Bayesian quantile regression feasible and flexible. Our method can be generalized to other applications that involve spatial correlation along irregular contours or in discontinuous spatial domains. Our results demonstrate the usefulness and effectiveness of the proposed methodology. • We propose a geoadditive model with spatial random effects to model the earthquake distribution in Mainland China. • The error is modeled an infinite mixture of Gaussian distributions with a stochastic constraint that ensures inference on the quantiles of interest. The spatial random effects are used to capture individual area effects which allow for heterogeneity among regions. • The proposed method not only allows for a full span of quantile-restricted error distributions, but also separates a large-scale geographical trend from local spatial correlation. [ABSTRACT FROM AUTHOR]