In analysis of longitudinal data, it is often assumed that observation times are predetermined and are the same across study subjects. Such an assumption, however, is often violated in practice. As a result, the observation times may be highly irregular. It is well known that if the sampling scheme is correlated with the outcome values, the usual statistical analysis may yield bias. In this article, we propose joint modeling and analysis of longitudinal data with possibly informative observation times via latent variables. A two-step estimation procedure is developed for parameter estimation. We show that the resulting estimators are consistent and asymptotically normal, and that the asymptotic variance can be consistently estimated using the bootstrap method. Simulation studies and a real data analysis demonstrate that our method performs well with realistic sample sizes and is appropriate for practical use.

In this paper, we investigate an energy cost minimization problem for a smart home in the absence of a building thermal dynamics model with the consideration of a comfortable temperature range. Due to the existence of model uncertainty, parameter uncertainty (e.g., renewable generation output, nonshiftable power demand, outdoor temperature, and electricity price) and temporally-coupled operational constraints, it is very challenging to determine the optimal energy management strategy for scheduling Heating, Ventilation, and Air Conditioning (HVAC) systems and energy storage systems in the smart home. To address the challenge, we first formulate the above problem as a Markov decision process, and then propose an energy management strategy based on Deep Deterministic Policy Gradients (DDPG). It is worth mentioning that the proposed strategy does not require the prior knowledge of uncertain parameters and building thermal dynamics model. Simulation results based on real-world traces demonstrate the effectiveness and robustness of the proposed strategy.

In this paper, we investigate the problem of minimizing the sum of energy cost and thermal discomfort cost in a long-term time horizon for a sustainable smart home with a Heating, Ventilation, and Air Conditioning (HVAC) load. Specifically, we first formulate a stochastic program to minimize the time average expected total cost with the consideration of uncertainties in electricity price, outdoor temperature, renewable generation output, electrical demand, the most comfortable temperature level, and home occupancy state. Then, we propose an online energy management algorithm based on the framework of Lyapunov optimization techniques without the need to predict any system parameters. The key idea of the proposed algorithm is to construct and stabilize four queues associated with indoor temperature, electric vehicle charging, and energy storage. Moreover, we theoretically analyze the feasibility and performance guarantee of the proposed algorithm. Extensive simulations based on real-world traces show the effectiveness of the proposed algorithm.

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Empirical likelihood inference is developed for censored survival data under the linear transformation models, which generalize Cox's [Regression models and life tables (with Discussion), J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] proportional hazards model. We show that the limiting distribution of the empirical likelihood ratio is a weighted sum of standard chi-squared distribution. Empirical likelihood ratio tests for the regression parameters with and without covariate adjustments are also derived. Simulation studies suggest that the empirical likelihood ratio tests are more accurate (under the null hypothesis) and powerful (under the alternative hypothesis) than the normal approximation based tests of Chen et al. [Semiparametric of transformation models with censored data, Biometrika 89 (2002) 659-668] when the model is different from the proportional hazards model and the proportion of censoring is high.

Abstract-Data center operators are typically faced with three significant problems when running their data centers, i.e., rising electricity bills, growing carbon footprints and unexpected power outages. To mitigate these issues, running data centers in microgrids is a good choice since microgrids can enhance the energy efficiency, sustainability and reliability of electrical services. Thus, in this paper, we investigate the problem of energy management for multiple data center microgrids. Specifically, we intend to minimize the long-term operational cost of data center microgrids by taking into account the uncertainties in electricity prices, renewable outputs and data center workloads. We first formulate a stochastic programming problem with the considerations of many factors, e.g., providing heterogeneous service delay guarantees for batch workloads, interactive workload allocation, batch workload shedding, electricity buying/selling, battery charging/discharging efficiency, and the ramping constraints of backup generators. Then, we design a realtime and distributed algorithm for the formulated problem based on Lyapunov optimization technique and a variant of alternating direction method of multipliers (ADMM). Moreover, the performance guarantees provided by the proposed algorithm are analyzed. Extensive simulation results indicate the effectiveness of the proposed algorithm in operational cost reduction for data center microgrids.