Weak convergence of non-stationary multivariate marked processes with applications to martingale testing

This paper establishes the weak convergence of a class of marked empirical processes of possibly non-stationary and/or non-ergodic multivariate time series sequences under martingale conditions. The assumptions involved are similar to those in Brown's martingale central limit theorem. In particular, no mixing conditions are imposed. As an application, we propose a test statistic for the martingale hypothesis and we derive its asymptotic null distribution. Finally, a Monte Carlo study shows that the asymptotic results provide good approximations for small and moderate sample sizes. An application to the S&P 500 is also considered.     

广义Taylor映射与Hénon映射具有混沌条件的改进

本文进一步讨论了近年来动力系统中关于对具有混沌现象的Taylor映射,Henon映射等函数所做的研究,并着重分析了所讨论函数的参数.     

Solving the Problem of Rerostering Nurse Schedules with Hard Constraints: New Multicommodity Flow Models

The problem of rerostering nurse schedules arises in hospitals when at least one nurse informs that she will be unable to perform the shifts assigned to her on one or more future work days. As a result, the current roster must be rebuilt in accordance with labour contract rules and institutional requirements. All such restraints are regarded as hard constraints. However, major alterations in the previously assigned nurse schedules must be avoided. This paper is based on a case study of a public hospital in Portugal. It presents two new integer multicommodity flow formulations for the rerostering problem, besides a computational experiment performed using real data. The first model is based on a directed multilevel acyclic network. The aggregation of nodes in this network led to the second model. The results obtained show that the second integer multicommodity flow formulation outperforms the first, both in terms of solution quality, as well as in computational time.     

Infinite Server Queues with Synchronized Departures Driven by a Single Point Process

We analyze an infinite-server queueing model with synchronized arrivals and departures driven by the point process {T _n } according to the following rules. At time T _n , a single customer (or a batch of size β _n ) arrives to the system. The service requirement of the ith customer in the nth batch is σ _i,n . All customers enter service immediately upon arrival but each customer leaves the system at the first epoch of the point process {T _n } which occurs after his service requirement has been satisfied. For this system the queue length process and the statistics of the departing batches of customers are investigated under various assumptions for the statistics of the point process {T _n }, the incoming batch sequence {β _n }, and the service sequence {σ _i,n }. Results for the asymptotic distribution of the departing batches when the service times are long compared to the interarrival times are also derived.     

On Generalized Linearity of Quadratic Fractional Functions

Quadratic fractional functions are proved to be quasilinear if and only if they are pseudo-linear. For these classes of functions, some characterizations are provided by means of the inertia of the quadratic form and the behavior of the gradient of the function itself. The study is then developed showing that generalized linear quadratic fractional functions share a particular structure. Therefore it is possible to suggest a sort of “canonical form” for those functions. A wider class of functions given by the sum of a quadratic fractional function and a linear one is also studied. In this case generalized linearity is characterized by means of simple conditions. Finally, it is deepened on the role played by generalized linear quadratic fractional functions in optimization problems.     

Least Squares Convex-Concave Data Smoothing

We consider n noisy measurements of a smooth (unknown) function, which suggest that the graph of the function consists of one convex and one concave section. Due to the noise the sequence of the second divided differences of the data exhibits more sign changes than those expected in the second derivative of the underlying function. We address the problem of smoothing the data so as to minimize the sum of squares of residuals subject to the condition that the sequence of successive second divided differences of the smoothed values changes sign at most once. It is a nonlinear problem, since the position of the sign change is also an unknown of the optimization process. We state a characterization theorem, which shows that the smoothed values can be derived by at most 2n – 2 quadratic programming calculations to subranges of data. Then, we develop an algorithm that solves the problem in about O(n ²) computer operations by employing several techniques, including B-splines, the use of active sets, quadratic programming and updating methods. A Fortran program has been written and some of its numerical results are presented. Applications of the smoothing technique may be found in scientific, economic and engineering calculations, when a potential shape for the underlying function is an S-curve. Generally, the smoothing calculation may arise from processes that show initially increasing and then decreasing rates of change.     

A flexible adaptive memory-based algorithm for real-life transportation operations: Two case studies from dairy and construction sector

Effective routing of vehicles remains a focal goal of all modern enterprises, thriving for excellence in project management with minimal investment and operational costs. This paper proposes a metaheuristic methodology for solving a practical variant of the well-known Vehicle Routing Problem, called Heterogeneous Fixed Fleet VRP (HFFVRP). Using a two-phase construction heuristic, called GEneralized ROute Construction Algorithm (GEROCA), the proposed metaheuristic approach enhances its flexibility to easily adopt various operational constraints. Via this approach, two real-life distribution problems faced by a dairy and a construction company were tackled and formulated as HFFVRP. Computational results on the aforementioned case studies show that the proposed metaheuristic approach (a) consistently outperforms previous published metaheuristic approaches we have developed to solve the HFFVRP, and (b) substantially improves upon the current practice of the company. The key result that impressed both companies’ management was the improvement over the bi-objective character of their problems: the minimization of the total distribution cost as well as the minimization of the number of the given heterogeneous number of vehicles used.     

A bivariate interval censorship model for partnership formation

We consider a statistical problem of estimating a bivariate age distribution of newly formed partnership. The study is motivated by a type of data that consist of uncensored, right-censored, left-censored, interval-censored and missing observations in the coordinates of a bivariate random vector. A model is proposed for formulating such type of data. A feasible algorithm to estimate the generalized MLE (GMLE) of the bivariate distribution function is also proposed. We establish asymptotic properties for the GMLE under a discrete assumption on the underlying distributions and apply the method to the data set.     

Axiomatic rank-dependent means

This paper provides an axiomatization for the implicit rank-dependent mean value, which class includes a number of mean values that have appeared in statistics, in utility theory and in the theory of income inequality measurement.