On risk-averse maximum weighted subgraph problems

In this work, we consider a class of risk-averse maximum weighted subgraph problems (R-MWSP). Namely, assuming that each vertex of the graph is associated with a stochastic weight, such that the joint distribution is known, the goal is to obtain a subgraph of minimum risk satisfying a given hereditary property. We employ a stochastic programming framework that is based on the formalism of modern theory of risk measures in order to find minimum-risk hereditary structures in graphs with stochastic vertex weights. The introduced form of risk function for measuring the risk of subgraphs ensures that optimal solutions of R-MWS problems represent maximal subgraphs. A graph-based branch-and-bound (BnB) algorithm for solving the proposed problems is developed and illustrated on a special case of risk-averse maximum weighted clique problem. Numerical experiments on randomly generated Erdös-Rényi graphs demonstrate the computational performance of the developed BnB.     

Efficiency of the generalized difference-based Liu estimators in semiparametric regression models with correlated errors

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in the semiparametric regression model when the errors are correlated. A generalized difference-based Liu estimator is defined for the vector parameter β in the semiparametric regression model. Under the linear nonstochastic constraint Rβ=r, the generalized restricted difference-based Liu estimator is given. The risk function for the β?_GRD(η) associated with weighted balanced loss function is presented. The performance of the proposed estimators is evaluated by a simulated data set.     

The Effectiveness of Multistage Ranked Set Sampling in Stratifying the Population

The spectral analysis of Gaussian linear time-series processes is usually based on uni-frequential tools because the spectral density functions of degree 2 and higher are identically zero and there is no polyspectrum in this case. In finite samples, such an approach does not allow the resolution of closely adjacent spectral lines, except by using autoregressive models of excessively high order in the method of maximum entropy. In this article, multi-frequential periodograms designed for the analysis of discrete and mixed spectra are defined and studied for their properties in finite samples. For a given vector of frequencies ω, the sum of squares of the corresponding trigonometric regression model fitted to a time series by unweighted least squares defines the multi-frequential periodogram statistic IM(ω). When ω is unknown, it follows from the properties of nonlinear models whose parameters separate (i.e., the frequencies and the cosine and sine coefficients here) that the least-squares estimator of frequencies is obtained by maximizing I ^M(ω). The first-order, second-order and distribution properties of I ^M(ω) are established theoretically in finite samples, and are compared with those of Schuster's uni-frequential periodogram statistic. In the multi-frequential periodogram analysis, the least-squares estimator of frequencies is proved to be theoretically unbiased in finite samples if the number of periodic components of the time series is correctly estimated. Here, this number is estimated at the end of a stepwise procedure based on pseudo-Flikelihood ratio tests. Simulations are used to compare the stepwise procedure involving I ^M(ω) with a stepwise procedure using Schuster's periodogram, to study an approximation of the asymptotic theory for the frequency estimators in finite samples in relation to the proximity and signal-to-noise ratio of the periodic components, and to assess the robustness of I ^M(ω) against autocorrelation in the analysis of mixed spectra. Overall, the results show an improvement of the new method over the classical approach when spectral lines are adjacent. Finally, three examples with real data illustrate specific aspects of the method, and extensions (i.e., unequally spaced observations, trend modeling, replicated time series, periodogram matrices) are outlined.     

Three New Multivariate Process Capability Indices

Different multivariate process capability indices are developed by researchers to evaluate process capability when vectors of quality characteristics are considered in a study. This article presents three indices referred to as NCpM, MCpM, and NMC _PM in order to evaluate process capability in multivariate environment. The performance of the proposed indices is investigated numerically. Simulation results indicate that the proposed indices have descended estimation error and improved performance compared to the existing ones. These results can be important to researchers and practitioners who are interested in evaluating process capability in multivariate domain.     

Spatial smoothing of low birth weight rate in Bangladesh using Bayesian hierarchical model

The term low birth weight refers an event where a newborn baby has a weight that is less than 2500?g. This is an essential indicator while the interest is in public health issues such as infant mortality, maternal complications, and antenatal care, etc. of a country, particularly, for a developing country like Bangladesh. The regional development programs are in the current priority list of Bangladesh government and other policy makers. Many of such regional development programs may need the spatial distribution of relative risk for low birth weight that can be obtained by mapping the risks over small area domains like the districts of Bangladesh. This study aims to find whether is there any spatial dependence among the relative risks of low birth weight for the districts of Bangladesh. This has been investigated using Moran's I statistic and a significant spatial dependence in the relative risks was found. Then, attempt has been made to rediscover the spatial distribution based on the idea of spatial smoothing. A Bayesian hierarchical model is used considering percent received antenatal care and female labor force participation as covariates to smooth the observed relative risks of low birth weight in 64 districts of Bangladesh. Revised spatial distribution taking the spatial dependence under consideration through intrinsic conditional autoregressive model is derived and showed in choropleth map along with its different behaviors.     

Majorization and the spectral radius of starlike trees

A starlike tree is a tree with exactly one vertex of degree greater than two. The spectral radius of a graph G, that is denoted by \(\lambda (G)\), is the largest eigenvalue of G. Let k and \(n_1,\ldots ,n_k\) be some positive integers. Let \(T(n_1,\ldots ,n_k)\) be the tree T (T is a path or a starlike tree) such that T has a vertex v so that \(T{\setminus } v\) is the disjoint union of the paths \(P_{n_1-1},\ldots ,P_{n_k-1}\) where every neighbor of v in T has degree one or two. Let \(P=(p_1,\ldots ,p_k)\) and \(Q=(q_1,\ldots ,q_k)\), where \(p_1\ge \cdots \ge p_k\ge 1\) and \(q_1\ge \cdots \ge q_k\ge 1\) are integer. We say P majorizes Q and let \(P\succeq _M Q\), if for every j, \(1\le j\le k\), \(\sum _{i=1}^{j}p_i\ge \sum _{i=1}^{j}q_i\), with equality if \(j=k\). In this paper we show that if P majorizes Q, that is \((p_1,\ldots ,p_k)\succeq _M(q_1,\ldots ,q_k)\), then \(\lambda (T(q_1,\ldots ,q_k))\ge \lambda (T(p_1,\ldots ,p_k))\).     

Robust allocation of a defensive budget considering an attacker's private information

Attackers' private information is one of the main issues in defensive resource allocation games in homeland security. The outcome of a defense resource allocation decision critically depends on the accuracy of estimations about the attacker's attributes. However, terrorists' goals may be unknown to the defender, necessitating robust decisions by the defender. This article develops a robust-optimization game-theoretical model for identifying optimal defense resource allocation strategies for a rational defender facing a strategic attacker while the attacker's valuation of targets, being the most critical attribute of the attacker, is unknown but belongs to bounded distribution-free intervals. To our best knowledge, no previous research has applied robust optimization in homeland security resource allocation when uncertainty is defined in bounded distribution-free intervals. The key features of our model include (1) modeling uncertainty in attackers' attributes, where uncertainty is characterized by bounded intervals; (2) finding the robust-optimization equilibrium for the defender using concepts dealing with budget of uncertainty and price of robustness; and (3) applying the proposed model to real data.     

A new four-parameter lifetime distribution

Generalizing lifetime distributions is always precious for applied statisticians. In this paper, we introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley geometric (EPLG) distribution, obtained by compounding EPL and geometric distributions. The new distribution arises in a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The distribution exhibits decreasing, increasing, unimodal and bathtub-shaped hazard rate functions, depending on its parameters. It contains several lifetime distributions as particular cases: EPL, new generalized Lindley, generalized Lindley, power Lindley and Lindley geometric distributions. We derive several properties of the new distribution such as closed-form expressions for the density, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Simulation studies are also provided. Finally, two real data applications are given for showing the flexibility and potentiality of the new distribution.     

Comparison between Bayesian approach and frequentist methods for estimating relative risk in randomized controlled trials: a simulation study

Relative risks (RRs) are often considered as preferred measures of association in randomized controlled trials especially when the binary outcome of interest is common. To directly estimate RRs, log-binomial regression has been recommended. Although log-binomial regression is a special case of generalized linear models, it does not respect the natural parameter constraints, and maximum likelihood estimation is often subject to numerical instability that leads to convergence problems. Alternative methods for solving log-binomial regression convergence problems have been proposed. A Bayesian approach also was introduced, but the comparison between this method and frequentist methods has not been fully explored. We compared five frequentist and one Bayesian methods for estimating RRs under a variety of scenario. Based on our simulation study, there is not a method that can perform well based on different statistical properties, but COPY 1000 and modified log-Poisson regression can be considered in practice.     

A recursive approach for lot sentencing problem in the presence of inspection errors

In this paper, a new sequential acceptance sampling plans in the presence of inspection errors is developed. A suitable profit objective function is employed for optimizing the lot sentencing problem. A backward recursive approach is applied for obtaining the profit of different decisions in each stage of sampling. Required probabilities are obtained using Bayesian rule. A case study is solved for illustrating the application of proposed models and sensitivity analysis are carried out on the parameters of the proposed methodologies and the behaviour of models by changing the parameters are investigated.