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In this paper, we focus on the partially linear varying-coefficient quantile regression model when the data are right censored and the censoring indicator is missing at random. Based on the calibration and imputation methods, a three-stage approach is proposed to construct the estimators of the linear part and the nonparametric varying-coefficient function for this model . At the same time, we discuss the variable selection of the covariates in the linear part by adopting adaptive LASSO penalty. Under appropriate assumptions, the asymptotic normality of the proposed estimators is established, and the penalized estimators are proven to have the oracle property. Simulation study and a real data analysis are conducted to evaluate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

This paper presents a general result that allows for establishing a link between the Kolmogorov–Marcinkiewicz– Zygmund strong law of large numbers and Feller’s strong law of large numbers in a Banach space setting. Let { X , X n ; n ≥ 1 } be a sequence of independent and identically distributed Banach space valued random variables and set S n = ∑ i = 1 n X i , n ≥ 1 . Let { a n ; n ≥ 1 } and { b n ; n ≥ 1 } be increasing sequences of positive real numbers such that lim n → ∞ a n = ∞ and b n ∕ a n ; n ≥ 1 is a nondecreasing sequence. We show that S n − n E X I { ‖ X ‖ ≤ b n } b n → 0 almost surely for every Banach space valued random variable X with ∑ n = 1 ∞ P ( ‖ X ‖ > b n ) < ∞ if S n ∕ a n → 0 almost surely for every symmetric Banach space valued random variable X with ∑ n = 1 ∞ P ( ‖ X ‖ > a n ) < ∞ . To establish this result, we invoke two tools (obtained recently by Li, Liang, and Rosalsky): a symmetrization procedure for the strong law of large numbers and a probability inequality for sums of independent Banach space valued random variables. [ABSTRACT FROM AUTHOR]

In this note, general symmetrization procedures for both the weak and strong laws of large numbers concerning the row sums from arrays of rowwise independent Banach space valued random variables are established. Necessary and sufficient conditions are provided for the weak and strong laws of large numbers to hold in terms of corresponding laws of large numbers for a symmetrized version of the array. Several corollaries of the main result are provided. [ABSTRACT FROM AUTHOR]

Abstract: In a recent paper by Chen (in press) the limit law of the iterated logarithm for the partial sums of i.i.d. real-valued random variables has been established. In this note we look at the corresponding problem in Banach space setting. Let be a real separable Banach space with topological dual . Let be a sequence of i.i.d. -valued random variables and set and . We show that provided that where and is the unit ball of . [Copyright &y& Elsevier]

Abstract: Let be a field of negatively associated random variables. Set , . Under some suitable conditions, we show that is a necessary and sufficient criteria for the almost sure central limit theorem, i.e.  where is the standard normal distribution function,  and  , , . In particular, we obtain here the almost sure central limit theorem for negatively associated fields that assures the usual central limit theorem. [Copyright &y& Elsevier]

Software project scheduling is the problem of allocating employees to tasks in a software project. Due to the large scale of current software projects, many studies have investigated the use of optimization algorithms to find good software project schedules. However, despite the importance of human factors to the success of software projects, existing work has considered only a limited number of human properties when formulating software project scheduling as an optimization problem. Moreover, the changing environments of software companies mean that software project scheduling is a dynamic optimization problem. However, there is a lack of effective dynamic scheduling approaches to solve this problem. This work proposes a more realistic mathematical model for the dynamic software project scheduling problem. This model considers that skill proficiency can improve over time and, different from previous work, it considers that such improvement is affected by the employees’ properties of motivation and learning ability, and by the skill difficulty. It also defines the objective of employees’ satisfaction with the allocation. It is considered together with the objectives of project duration, cost, robustness and stability under a variety of practical constraints. To adapt schedules to the dynamically changing software project environments, a multi-objective two-archive memetic algorithm based on Q-learning (MOTAMAQ) is proposed to solve the problem in a proactive-rescheduling way. Different from previous work, MOTAMAQ learns the most appropriate global and local search methods to be used for different software project environment states by using Q-learning. Extensive experiments on 18 dynamic benchmark instances and 3 instances derived from real-world software projects were performed. A comparison with seven other meta-heuristic algorithms shows that the strategies used by our novel approach are very effective in improving its convergence performance in dynamic environments, while maintaining a good distribution and spread of solutions. The Q-learning-based learning mechanism can choose appropriate search operators for the different scheduling environments. We also show how different trade-offs among the five objectives can provide software managers with a deeper insight into various compromises among many objectives, and enabling them to make informed decisions. [ABSTRACT FROM AUTHOR]