Dual divergence estimators and tests: Robustness results

The class of dual ?-divergence estimators (introduced in Broniatowski and Keziou (2009) [5]) is explored with respect to robustness through the influence function approach. For scale and location models, this class is investigated in terms of robustness and asymptotic relative efficiency. Some hypothesis tests based on dual divergence criteria are proposed and their robustness properties are studied. The empirical performances of these estimators and tests are illustrated by Monte Carlo simulation for both non-contaminated and contaminated data.     

A choice of forcing terms in inexact Newton method

Inexact Newton method is one of the effective tools for solving systems of nonlinear equations. In each iteration step of the method, a forcing term, which is used to control the accuracy when solving the Newton equations, is required. The choice of the forcing terms is of great importance due to their strong influence on the behavior of the inexact Newton method, including its convergence, efficiency, and even robustness. To improve the efficiency and robustness of the inexact Newton method, a new strategy to determine the forcing terms is given in this paper. With the new forcing terms, the inexact Newton method is locally Q-superlinearly convergent. Numerical results are presented to support the effectiveness of the new forcing terms.     

集装箱码头泊位计划的鲁棒优化模型

针对集装箱码头作业中的不确定性因素,构建泊位计划的鲁棒优化模型与算法,目的是降低不确定性因素对集装箱码头作业系统的影响。首先,提出泊位计划鲁棒性度量指标,利用算例对各指标的效果进行分析。在此基础上,设计泊位计划鲁棒优化的两阶段优化算法。算法的第一阶段不考虑泊位计划的鲁棒性,以船舶总延误时间最小为目标;算法的第二阶段以所选择的鲁棒性指标最大为目标,以第一阶段获得的船舶总延误时间为约束条件,获得鲁棒调度方案。最后,研究作业资源(装卸桥数量)的变化对泊位计划鲁棒性的影响。算例分析表明,权重松弛量是有效的度量泊位计划鲁棒性的指标,两阶段算法可以有效解决泊位计划鲁棒优化问题。     

Robust variable selection for finite mixture regression models

Finite mixture regression (FMR) models are frequently used in statistical modeling, often with many covariates with low significance. Variable selection techniques can be employed to identify the covariates with little influence on the response. The problem of variable selection in FMR models is studied here. Penalized likelihood-based approaches are sensitive to data contamination, and their efficiency may be significantly reduced when the model is slightly misspecified. We propose a new robust variable selection procedure for FMR models. The proposed method is based on minimum-distance techniques, which seem to have some automatic robustness to model misspecification. We show that the proposed estimator has the variable selection consistency and oracle property. The finite-sample breakdown point of the estimator is established to demonstrate its robustness. We examine small-sample and robustness properties of the estimator using a Monte Carlo study. We also analyze a real data set.     

Uniform random number generation

In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in an appropriate way. In this paper, we examine practical ways of generating (deterministic approximations to) such uniform variates on a computer. We compare them in terms of ease of implementation, efficiency, theoretical support, and statistical robustness. We look in particular at several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear congruential over fields of formal series, and combined generators, and show how all of them can be analyzed in terms of their lattice structure. We also mention other classes of generators, like non-linear generators, discuss other kinds of theoretical and empirical statistical tests, and give a bibliographic survey of recent papers on the subject.     

Cost,revenue and profit efficiency measurement in DEA: A directional distance function approach

Estimation of efficiency of firms in a non-competitive market characterized by heterogeneous inputs and outputs along with their varying prices is questionable when factor-based technology sets are used in data envelopment analysis (DEA). In this scenario, a value-based technology becomes an appropriate reference technology against which efficiency can be assessed. In this contribution, the value-based models of Tone (2002) are extended in a directional DEA set up to develop new directional cost- and revenue-based measures of efficiency, which are then decomposed into their respective directional value-based technical and allocative efficiencies. These new directional value-based measures are more general, and include the existing value-based measures as special cases. These measures satisfy several desirable properties of an ideal efficiency measure. These new measures are advantageous over the existing ones in terms of (1) their ability to satisfy the most important property of translation invariance; (2) choices over the use of suitable direction vectors in handling negative data; and (3) flexibility in providing the decision makers with the option of specifying preferable direction vectors to incorporate their preferences. Finally, under the condition of no prior unit price information, a directional value-based measure of profit inefficiency is developed for firms whose underlying objectives are profit maximization. For an illustrative empirical application, our new measures are applied to a real-life data set of 50 US banks to draw inferences about the production correspondence of banking industry.     

Data envelopment analysis with heterogeneous data: an application

The effects of data heterogeneity on the efficiency estimate by data envelopment analysis are evaluated here in terms of empirical applications in the computer industry. Scale or size variations of firms and heteroscedasticity are the two forms of heterogeneity considered here. Our empirical results show that the adverse effects of data heterogeneity can be considerably reduced by the methods suggested here.     

投资者情绪对科创板市场收益率的影响——基于文本数据挖掘视角

本文以科创板市场为主要研究对象,基于文本数据挖掘方法探究了新冠疫情发生前和疫情期间投资者情绪对市场收益率的影响及其作用机制。利用东方财富股吧2019年7月至2020年3月的日度科创板股票评论数据,基于Bi-LSTM深度学习技术对文本数据情感倾向进行分类,建立投资者情绪指数。通过构建双向固定效应的联立方程模型,采用2SLS方法估计投资者情绪对科创板市场收益率的作用,并检验在经济平稳运行和受新冠疫情冲击期间该作用的差异性。实证分析及稳健性检验的结果均表明,投资者情绪通过影响交易量进而影响科创板股票市场收益率,这种正向作用在1%的置信水平下显著。此外,投资者情绪对科创板收益率的影响在经济平稳运行和受新冠疫情冲击期间均保持稳健,且在新冠疫情期间作用更强。本研究成果对于新冠疫情期间我国证券市场监管层完善科创板交易机制,以及对中小投资者优化投资战略具有重要意义。     

Discounted cost optimality problem: stability with respect to weak metrics

We find inequalities to estimate the stability (robustness) of a discounted cost optimization problem for discrete-time Markov control processes on a Borel state space. The one stage cost is allowed to be unbounded. Unlike the known results in this area we consider a perturbation of transition probabilities measured by the Kantorovich metric, closely related to the weak convergence. The results obtained make possible to estimate the vanishing rate of the stability index when approximation is made through empirical measures.     

Multiple objectives decomposition–coordination methods for hierarchical organizations

In this paper, the integration of goal programming models and hierarchical programming models is analyzed. The systems under study are assumed to consist of interconnected subsystems with multiple goals in each. Three possible cases regarding the number of decision makers will be considered: (1) one decision maker for the overall goals and one decision maker for each subsystem, (2) conflicting decision makers who are interested in their subsystems, and (3) just one decision maker for the overall system. Next, conditions are stated under which the problem of obtaining satisfying solutions for problems (1) and (3) can be reduced to the problem of obtaining satisfying solutions for the case (2). In order to determine such solutions, hierarchical techniques which exploit the structure of a decomposable system are analyzed. The empirical implementation of the two algorithms proposed shows their efficiency in terms of processing time.     

A globally convergent algorithm for computing fixed points of C2 maps

Chow, Mallet-Paret, and Yorke have recently proposed in abstract terms an algorithm for computing Brouwer fixed points of C² maps. A numerical implementation of that algorithm is presented here. Careful attention has been paid to computational efficiency, accuracy, and robustness. Some convergence theorems and results of numerical tests are also included.     

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In this article, we develop efficient robust method for estimation of mean and covariance simultaneously for longitudinal data in regression model. Based on Cholesky decomposition for the covariance matrix and rewriting the regression model, we propose a weighted least square estimator, in which the weights are estimated under generalized empirical likelihood framework. The proposed estimator obtains high efficiency from the close connection to empirical likelihood method, and achieves robustness by bounding the weighted sum of squared residuals. Simulation study shows that, compared to existing robust estimation methods for longitudinal data, the proposed estimator has relatively high efficiency and comparable robustness. In the end, the proposed method is used to analyse a real data set.     

Meshless method with ridge basis functions

Meshless collocation methods for the numerical solutions of PDEs are increasingly adopted due to their advantages including efficiency and flexibility, and radial basis functions are popularly employed to represent the solutions of PDEs. Motivated by the advantages of ridge basis function representation of a given function, such as the connection to neural network, fast convergence as the number of terms is increased, better approximation effects and various applications in engineering problems, a meshless method is developed based on the collocation method and ridge basis function interpolation. This method is a truly meshless technique without mesh discretization: it neither needs the computation of integrals, nor requires a partition of the region and its boundary. Moreover, the method is applied to elliptic equations to examine its appropriateness, numerical results are compared to that obtained from other (meshless) methods, and influence factors of accuracy for numerical solutions are analyzed.     

A Class of Robust Principal Component Vectors

This paper is concerned with a study of robust estimation in principal component analysis. A class of robust estimators which are characterized as eigenvectors of weighted sample covariance matrices is proposed, where the weight functions recursively depend on the eigenvectors themselves. Also, a feasible algorithm based on iterative reweighting of the covariance matrices is suggested for obtaining these estimators in practice. Statistical properties of the proposed estimators are investigated in terms of sensitivity to outliers and relative efficiency via their influence functions, which are derived with the help of Stein's lemma. We give a simple condition on the weight functions which ensures robustness of the estimators. The class includes, as a typical example, a method by the self-organizing rule in the neural computation. A numerical experiment is conducted to confirm a rapid convergence of the suggested algorithm.     

An Inverse Reliability-based Approach for Designing under Uncertainty with Application to Robust Piston Design

In this work, we propose an optimization framework for designing under uncertainty that considers both robustness and reliability issues. This approach is generic enough to be applicable to engineering design problems involving nonconvex objective and constraint functions defined in terms of random variables that follow any distribution. The problem formulation employs an Inverse Reliability Strategy that uses percentile performance to address both robustness objectives and reliability constraints. Robustness is achieved through a design objective that evaluates performance variation as a percentile difference between the right and left trails of the specified goals. Reliability requirements are formulated as Inverse Reliability constraints that are based on equivalent percentile performance levels. The general proposed approach first approximates the formulated problem via a Gaussian Kriging model. This is then used to evaluate the percentile performance characteristics of the different measures inherent in the problem formulation for various design variable settings via a Most Probable Point of Inverse Reliability search algorithm. By using these percentile evaluations in concert with the response surface methodology, a polynomial programming approximation is generated. The resulting problem formulation is finally solved to global optimality using the Reformulation–Linearization Technique (RLT) approach. We demonstrate this overall proposed approach by applying it to solve the problem of reducing piston slap, an undesirable engine noise due to the secondary motion of a piston within a cylinder.     

Algorithms for linear programming with linear complementarity constraints

Linear programming with linear complementarity constraints (LPLCC) is an area of active research in Optimization, due to its many applications, algorithms, and theoretical existence results. In this paper, a number of formulations for important nonconvex optimization problems are first reviewed. The most relevant algorithms for computing a complementary feasible solution, a stationary point, and a global minimum for the LPLCC are also surveyed, together with some comments about their efficiency and efficacy in practice.     

A hybrid conjugate finite-step length method for robust and efficient reliability analysis

The robustness and efficiency of the first-order reliability method (FORM) are the important issues in the structural reliability analysis. In this paper, a hybrid conjugate search direction with finite-step length is proposed to improve the efficiency and robustness of FORM, namely hybrid conjugate finite-step length (CFSL-H). The conjugate scalar factor in CFSL-H is adaptively updated using two conjugate methods with a dynamic participation factor. The accuracy, efficiency and robustness of the CFSL-H are illustrated through the nonlinear explicit and structural implicit limit state functions with normal and non-normal random variables. The results illustrated that the proposed CFSL-H algorithm is more robust, efficient and accurate than the modified existing FORM algorithms for complex structural problems.     

DEA with efficiency classification preserving conditional convexity

We propose to relax the standard convexity property used in Data Envelopment Analysis (DEA) by imposing additional qualifications for feasibility of convex combinations. We specifically focus on a condition that preserves the Koopmans efficiency classification. This yields an efficiency classification preserving conditional convexity property, which is implied by both monotonicity and convexity, but not conversely. Substituting convexity by conditional convexity, we construct various empirical DEA approximations as the minimal sets that contain all DMUs and are consistent with the imposed production assumptions. Imposing an additional disjunctive constraint to standard convex DEA formulations can enforce conditional convexity. Computation of efficiency measures relative to conditionally convex production set can be performed through Disjunctive Programming (DP).     

Robust Solutions in Stochastic Linear Programming

The recent developments in stochastic linear programming are reviewed here broadly in their applied aspects. They include non-parametric methods which are applicable in situations of incomplete knowledge and partial uncertainty. This framework is shown to be most suitable for developing robust optimal solutions. For instance, a class of non-parametric methods based on the minimax principle and the criteria of stochastic dominance is developed here to illustrate its wide scope of application. It is shown that this class of methods provides a measure of robustness through the adoption of a cautious policy. Some examples are discussed using the recent field of data envelopment analysis.     

Two-dimensional efficiency decomposition to measure the demand effect in productivity analysis

This paper proposes a two-dimensional efficiency decomposition (2DED) of profitability for a production system to account for the demand effect observed in productivity analysis. The first dimension identifies four components of efficiency: capacity design, demand generation, operations, and demand consumption, using Network Data Envelopment Analysis (Network DEA). The second dimension decomposes the efficiency measures and integrates them into a profitability efficiency framework. Thus, each component’s profitability change can be analyzed based on technical efficiency change, scale efficiency change and allocative efficiency change. An empirical study based on data from 2006 to 2008 for the US airline industry finds that the regress of productivity is mainly caused by a demand fluctuation in 2007-2008 rather than technical regression in production capabilities.