Selection between proportional and stratified hazards models based on expected log-likelihood

The problem of selecting between semi-parametric and proportional hazards models is considered. We propose to make this choice based on the expectation of the log-likelihood (ELL) which can be estimated by the likelihood cross-validation (LCV) criterion. The criterion is used to choose an estimator in families of semi-parametric estimators defined by the penalized likelihood. A simulation study shows that the ELL criterion performs nearly as well in this problem as the optimal Kullback–Leibler criterion in term of Kullback–Leibler distance and that LCV performs reasonably well. The approach is applied to a model of age-specific risk of dementia as a function of sex and educational level from the data of a large cohort study.     

On models for continuous facility location with partial coverage

This paper presents a new concept of partial coverage distance, where demand points within a given threshold distance of a new facility are covered in the traditional sense, while non-covered demand points are penalized an amount proportional to their distance to the covered region. Two single facility location models, based on the minisum and minimax criteria, are formulated with the new distance function, and the structure of the models is analysed.     

Lattice preconditioning for the real relaxation branch-and-bound approach for integer least squares problems

The integer least squares problem is an important problem that arises in numerous applications. We propose a real relaxation-based branch-and-bound (RRBB) method for this problem. First, we define a quantity called the distance to integrality, propose it as a measure of the number of nodes in the RRBB enumeration tree, and provide computational evidence that the size of the RRBB tree is proportional to this distance. Since we cannot know the distance to integrality a priori, we prove that the norm of the Moore–Penrose generalized inverse of the matrix of coefficients is a key factor for bounding this distance, and then we propose a preconditioning method to reduce this norm using lattice reduction techniques. We also propose a set of valid box constraints that help accelerate the RRBB method. Our computational results show that the proposed preconditioning significantly reduces the size of the RRBB enumeration tree, that the preconditioning combined with the proposed set of box constraints can significantly reduce the computational time of RRBB, and that the resulting RRBB method can outperform the Schnorr and Eucher method, a widely used method for solving integer least squares problems, on some types of problem data.     

TOPSIS for bi-level MODM problems

TOPSIS (technique for order preference by similarity to ideal solution) is a multiple criteria method to identify solutions from a finite set of alternatives based upon simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. This paper proposes a fuzzy TOPSIS algorithm to solve bi-level multi-objective decision-making (BL-MODM) problems, and in which the objective function at each level are non-linear functions which are to be maximized. The proposed model for getting the satisfactory solution of the BL-MODM problems includes the membership functions for the upper level decision variables vector with possible tolerances, the membership function of the distance function from the positive ideal solution (PIS) and the membership function of the distance function from the negative ideal solution (NIS). A numerical illustrative example is given to clarify the proposed TOPSIS approach of this paper.     

Linear programming solutions and distance functions under a constant returns to scale technology

In this paper, we investigate the various relationships among the linear programming solutions of data envelopment analysis (DEA) models under a constant returns to scale technology. We derive the analytical relationships among the efficiency measures and the activity variables for four separate models: the input-based, the output-based, the hyperbolic, and the proportional distance functions. We apply our results in order to derive a test of consistency that can be used in assessing the returns to scale among differing DEA models.     

平行机的供应链排序

研究平行机环境下的供应链排序,即研究如何安排工件在平行机上加工,把加工完毕的工件分批发送给下游客户,使得生产排序费用和发送费用总和最少。这里,生产排序费用是用工件送到时间的函数表示;发送费用是由固定费用和与运输路径有关的可变费用两部分组成。研究以工件带权送到时间和作为生产排序费用的供应链排序问题,给出多项式时间近似算法,并分析算法性能比。     

Using the Hamming distance to extend TOPSIS in a fuzzy environment

Considering the fact that, in some cases, determining precisely the exact value of attributes is difficult and that their values can be considered as fuzzy data, this paper extends the TOPSIS method for dealing with fuzzy data, and an algorithm for determining the best choice among all possible choices when the data are fuzzy is also presented. In this approach, to identify the fuzzy ideal solution and fuzzy negative ideal solution, one of the Yager indices which is used for ordering fuzzy quantities in [0, 1] is applied. Using Yager’s index leads to a procedure for choosing fuzzy ideal and negative ideal solutions directly from the data for observed alternatives. Then, the Hamming distance is proposed for calculating the distance between two triangular fuzzy numbers. Finally, an application is given, to clarify the main results developed in the paper.     

Proportional odds frailty model and stochastic comparisons

In this paper, we present some distributional properties of the survival and frailty distribution involved in the proportional odds (PO) frailty model. Stochastic orderings are studied for this proportional odds frailty model. It is showed that negative dependence arises in the PO frailty model as opposed to the proportional hazard frailty model.     

Re-examination of Bregman functions and new properties of their divergences

ABSTRACT

The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the ‘Bregman function’). Bregman functions and divergences have been extensively investigated during the last decades and have found applications in optimization, operations research, information theory, nonlinear analysis, machine learning and more. This paper re-examines various aspects related to the theory of Bregman functions and divergences. In particular, it presents many sufficient conditions which allow the construction of Bregman functions in a general setting and introduces new Bregman functions (such as a negative iterated log entropy). Moreover, it sheds new light on several known Bregman functions such as quadratic entropies, the negative Havrda-Charvát-Tsallis entropy, and the negative Boltzmann-Gibbs-Shannon entropy, and it shows that the negative Burg entropy, which is not a Bregman function according to the classical theory but nevertheless is known to have ‘Bregmanian properties’, can, by our re-examination of the theory, be considered as a Bregman function. Our analysis yields several by-products of independent interest such as the introduction of the concept of relative uniform convexity (a certain generalization of uniform convexity), new properties of uniformly and strongly convex functions, and results in Banach space theory.     

A Weighted Likelihood Ratio of Two Related Negative Hypergeomeric Distributions

In this paper we consider some related negative hypergeometric distributions arising from the problem of sampling without replacement from an urn containing balls of different colours and in different proportions but stopping only after some specific number of balls of different colours have been obtained. With the aid of some simple recurrence relations and identities we obtain in the case of two colours the moments for the maximum negative hypergeometric distribution, the minimum negative hypergeometric distribution,the likelihood ratio negative hypergeometric distribution and consequently the likelihood proportional negative hypergeometric distributiuon. To the extent that the sampling scheme is applicable to modelling data as illustrated with a biological example and in fact many situations of estimating Bernoulli parameters for binary traits within a finite population, these are important first-step results.     

A queueing analysis of max-min fairness, proportional fairness and balanced fairness

We compare the performance of three usual allocations, namely max-min fairness, proportional fairness and balanced fairness, in a communication network whose resources are shared by a random number of data flows. The model consists of a network of processor-sharing queues. The vector of service rates, which is constrained by some compact, convex capacity set representing the network resources, is a function of the number of customers in each queue. This function determines the way network resources are allocated. We show that this model is representative of a rich class of wired and wireless networks. We give in this general framework the stability condition of max-min fairness, proportional fairness and balanced fairness and compare their performance on a number of toy networks.     

Co-variation for sensitivity analysis in Bayesian networks: Properties,consequences and alternatives

Upon varying parameters in a sensitivity analysis of a Bayesian network, the standard approach is to co-vary the parameters from the same conditional distribution such that their proportions remain the same. Alternative co-variation schemes are, however, possible. In this paper we investigate the properties of the standard proportional co-variation and introduce two alternative schemes: uniform and order-preserving co-variation. We theoretically investigate the effects of using alternative co-variation schemes on the so-called sensitivity function, and conclude that its general form remains the same under any linear co-variation scheme. In addition, we generalise the CD-distance for bounding global belief change to explicitly include the co-variation scheme under consideration. We prove a tight lower bound on this distance for parameter changes in single conditional probability tables.     

Three-Particle Problem with Pairwise Interactions Inversely Proportional to Squared Distance

The hyperharmonic method is used to investigate the three-particle Schrödinger and Faddeev equations with pairwise interactions inversely proportional to the squared distance. Exact solutions for such equations are constructed in the form of a product of the Bessel function depending on the hyperradius and a finite linear combination of the hyperharmonics. A criterion for the existence of such solutions is proved and analyzed.     

An informational distance for estimating the faithfulness of a possibility distribution,viewed as a family of probability distributions,with respect to data

An acknowledged interpretation of possibility distributions in quantitative possibility theory is in terms of families of probabilities that are upper and lower bounded by the associated possibility and necessity measures. This paper proposes an informational distance function for possibility distributions that agrees with the above-mentioned view of possibility theory in the continuous and in the discrete cases. Especially, we show that, given a set of data following a probability distribution, the optimal possibility distribution with respect to our informational distance is the distribution obtained as the result of the probability-possibility transformation that agrees with the maximal specificity principle. It is also shown that when the optimal distribution is not available due to representation bias, maximizing this possibilistic informational distance provides more faithful results than approximating the probability distribution and then applying the probability-possibility transformation. We show that maximizing the possibilistic informational distance is equivalent to minimizing the squared distance to the unknown optimal possibility distribution. Two advantages of the proposed informational distance function is that (i) it does not require the knowledge of the shape of the probability distribution that underlies the data, and (ii) it amounts to sum up the elementary terms corresponding to the informational distance between the considered possibility distribution and each piece of data. We detail the particular case of triangular and trapezoidal possibility distributions and we show that any unimodal unknown probability distribution can be faithfully upper approximated by a triangular distribution obtained by optimizing the possibilistic informational distance.     

On reduction of duality gap in quadratic knapsack problems

We investigate in this paper the duality gap between quadratic knapsack problem and its Lagrangian dual or semidefinite programming relaxation. We characterize the duality gap by a distance measure from set {0, 1} ⁿ to certain polyhedral set and demonstrate that the duality gap can be reduced by an amount proportional to the square of the distance. We further discuss how to compute the distance measure via cell enumeration method and to derive the corresponding improved upper bound of the problem.     

自由作业环境下的供应链排序问题

本文研究自由作业环境下的供应链排序问题,研究供应链的上游如何安排工件在自由作业机器上加工,把加工完毕的工件分批发送给下游,使得生产排序费用和发送费用总和最少.这里,生产排序费用是用工件送到时间的函数来表示;发送费用是由发送的固定费用和与运输路径有关的变化费用所组成.本文研究以工件最大送到时间为生产排序费用的自由作业供应链排序问题,在指出问题的NP困难性后,用动态规划算法构造多项式时间近似算法,并分析算法的性能比.本文最后还对特殊情形进行了讨论.     

On absolute ruin minimization under a diffusion approximation model

In this paper, we assume that the surplus process of an insurance entity is represented by a pure diffusion. The company can invest its surplus into a Black-Scholes risky asset and a risk free asset. We impose investment restrictions that only a limited amount is allowed in the risky asset and that no short-selling is allowed. We further assume that when the surplus level becomes negative, the company can borrow to continue financing. The ultimate objective is to seek an optimal investment strategy that minimizes the probability of absolute ruin, i.e. the probability that the liminf of the surplus process is negative infinity. The corresponding Hamilton-Jacobi-Bellman (HJB) equation is analyzed and a verification theorem is proved; applying the HJB method we obtain explicit expressions for the S-shaped minimal absolute ruin function and its associated optimal investment strategy. In the second part of the paper, we study the optimization problem with both investment and proportional reinsurance control. There the minimal absolute ruin function and the feedback optimal investment-reinsurance control are found explicitly as well.     

自由作业的供应链排序研究

研究一类集成工件加工和发送的供应链排序模型,即研究如何安排工件在自由作业机器上加工,把加工完毕的工件分批发送给下游客户,使得含生产排序费用和发送费用的目标函数最优.这里,分别取工件最大送到时间和平均送到时间为生产排序费用;而发送费用是由固定费用和与运输路径有关的变化费用组成.利用排序理论和动态规划方法,构造了自由作业供应链排序问题的多项式时间近似算法,并分析算法的性能比.     

Witnessed k-Distance

Distance functions to compact sets play a central role in several areas of computational geometry. Methods that rely on them are robust to the perturbations of the data by the Hausdorff noise, but fail in the presence of outliers. The recently introduced distance to a measure offers a solution by extending the distance function framework to reasoning about the geometry of probability measures, while maintaining theoretical guarantees about the quality of the inferred information. A combinatorial explosion hinders working with distance to a measure as an ordinary power distance function. In this paper, we analyze an approximation scheme that keeps the representation linear in the size of the input, while maintaining the guarantees on the inference quality close to those for the exact but costly representation.     

Optimal Dividend Payments in a Dual Risk Model with both Fixed and Proportional Costs

In this paper, we study the optimal dividend problem in a dual risk model, which might be appropriate for companies that have fixed expenses and occasional profits. Assuming that dividend payments are subject to both proportional and fixed transaction costs, our object is to maximize the expected present value of dividend payments until ruin, which is defined as the first time the company's surplus becomes negative. This optimization problem is formulated as a stochastic impulse control problem. By solving the corresponding quasi-variational inequality (QVI), we obtain the analytical solutions of the value function and its corresponding optimal dividend strategy when jump sizes are exponentially distributed.