Tolerance intervals for autoregressive models,with an application to hospital waiting lists

Long waiting lists are a symbol of inefficiencies of hospital services. The dynamics of waiting lists are complex, especially when trying to understand how the lists grow due to the demand of a particular treatment relative to a hospital's capacity. Understanding the uncertainty of forecasting growth/decline of waiting lists could help hospital managers with capacity planning. We address this uncertainty through the use of statistical tolerance intervals, which are intervals that contain a specified proportion of the sampled population at a given confidence level. Tolerance intervals are available for numerous settings, however, the approaches for autoregressive models are far more limited. This article fills that gap and establishes tolerance intervals for general AR(p) models, which may also have a mean or trend component present. A rigorous development of tolerance intervals in this setting is presented. Extensive simulation studies identify that good coverage properties are achieved when the AR process is stationary and the parameters of the AR model are well within the stationarity constraints. Otherwise, a bootstrap‐based correction can be applied to improve the coverage probabilities. Finally, the method is applied to the monthly number of patients on hospital waiting lists in England.     

A network efficiency measure with application to critical infrastructure networks

In this paper, we demonstrate how a new network performance/efficiency measure, which captures demands, flows, costs, and behavior on networks, can be used to assess the importance of network components and their rankings. We provide new results regarding the measure, which we refer to as the Nagurney–Qiang measure, or, simply, the N–Q measure, and a previously proposed one, which did not explicitly consider demands and flows. We apply both measures to such critical infrastructure networks as transportation networks and the Internet and further explore the new measure through an application to an electric power generation and distribution network in the form of a supply chain. The Nagurney and Qiang network performance/efficiency measure that captures flows and behavior can identify which network components, that is, nodes and links, have the greatest impact in terms of their removal and, hence, are important from both vulnerability as well as security standpoints.     

Nonparametric conditional autoregressive expectile model via neural network with applications to estimating financial risk

The parametric conditional autoregressive expectiles (CARE) models have been developed to estimate expectiles, which can be used to assess value at risk and expected shortfall. The challenge lies in parametric CARE modeling is the specification of a parametric form. To avoid any model misspecification, we propose a nonparametric CARE model via neural network. The nonparametric CARE model can be estimated by a classical gradient based nonlinear optimization algorithm, and the consistency of nonparametric conditional expectile estimators is established. We then apply the nonparametric CARE model to estimating value at risk and expected shortfall of six stock indices. Empirical results for the new model is competitive with those classical models and parametric CARE models. Copyright © 2016 John Wiley & Sons, Ltd.     

Mixture estimation with state-space components and Markov model of switching

The paper proposes a recursive algorithm for estimation of mixtures with state-space components and a dynamic model of switching. Bayesian methodology is adopted. The main features of the presented approach are: (i) recursiveness that enables a real-time performance of the algorithm; (ii) one-pass elaboration of the data sample; (iii) dynamic nature of the model of switching active components; (iv) orientation at explicit solutions with exploitation of numerical procedures only in those parts which cannot be computed analytically; (v) systematic approach to the Bayesian mixture estimation theory.     

Free trial or no free trial: Optimal software product design with network effects

A common business strategy to promote product adoption in software industry is to provide a free trial version with limited functionalities of the commercial product to increase the installed user base. The increase of user base will lead to higher value of the software because of positive network effects. However, offering a free trial version may cannibalize some demand of the commercial software. This paper examines the tradeoff between network effects and the cannibalization effect, and aims to uncover the conditions under which firms should introduce the free trial product. We find that when network intensity is strong, it is more profitable for a software monopoly to offer free trial than to segment the market with two versions of different qualities. In addition, this paper solves the joint decision problem of finding the optimal quality for the firm’s free trial software and the optimal price of its commercial product.     

Optimal worst-case pricing for a logit demand model with network effects

We consider optimal pricing problems for a product that experiences network effects. Given a price, the sales quantity of the product arises as an equilibrium, which may not be unique. In contrast to previous studies that take a best-case view when there are multiple equilibrium sales quantities, we maximize the seller’s revenue assuming that the worst-case equilibrium quantity will arise in response to a chosen price. We compare the best- and worst-case solutions, and provide asymptotic analysis of revenues.     

Modeling clustered binary data with nonparametric unobserved heterogeneity: An application to stock crash analysis

Various random effects models have been developed for clustered binary data; however, traditional approaches to these models generally rely heavily on the specification of a continuous random effect distribution such as Gaussian or beta distribution. In this article, we introduce a new model that incorporates nonparametric unobserved random effects on unit interval (0,1) into logistic regression multiplicatively with fixed effects. This new multiplicative model setup facilitates prediction of our nonparametric random effects and corresponding model interpretations. A distinctive feature of our approach is that a closed-form expression has been derived for the predictor of nonparametric random effects on unit interval (0,1) in terms of known covariates and responses. A quasi-likelihood approach has been developed in the estimation of our model. Our results are robust against random effects distributions from very discrete binary to continuous beta distributions. We illustrate our method by analyzing recent large stock crash data in China. The performance of our method is also evaluated through simulation studies.     

Reconstructing freeway travel times with a simplified network flow model alternating the adopted fundamental diagram

The present study summarises the travel time reconstruction performance of a network flow model by explicitly analysing the adopted fundamental diagram relation under congested and un-congested traffic patterns. The incorporated network flow model uses a discrete meso-simulation approach in which the anisotropic property of traffic flow and the uniform acceleration of vehicle packets are explicitly considered. The flow performances on link-route dynamics have been derived by reasonably alternating the adopted two-phase, i.e., congested and un-congested, fundamental relation of traffic flow. The linear speed–density relation with the creeping speed assumption is substituted with the triangular flow–density relation in order to investigate the performance of the network flow model in varying flow patterns. Applying the anisotropic mesoscopic model, the measure of travel time is obtained as a link performance from a simplified dynamic network loading process. Travel time reconstruction performance of the network flow model is sought considering the actual measures that are obtained by a probe vehicle, in addition to reconstructions by a macroscopic network flow model. The main improvements on travel time reconstruction process are encountered in terms of the computation load within the explicit analyses by the alternation of adopted two-phase fundamental diagram. Although the accuracies of the flow model with the adoption of two different fundamental diagrams are hard to differentiate, the computational burden of the simulation process by the triangular fundamental diagram is found to be considerably different.     

基于errors-in-variables的预测模型及其应用

预测是统计学实际应用的一个主要方面,多元线性回归预测是一种很好的方法,广泛地应用在各种实际领域,但其局限性及不足也是明显的。本文以一种新的观点认识数据,即认为变量的观测里均含有误差,同时认为不应删除经慎重选择进来的解释变量。为此,本文提出了一种新的多元预测方法———多元线性EIV预测。本文还考虑了新预测模型的一个实例应用,并从相对偏差上与多元回归预测进行了比较,从而揭示了多元线性EIV预测的先进性及较好的预测精度。     

A genetic algorithm for a single product network design model with lead time and safety stock considerations

We consider a two-stage supply chain with a production facility that replenishes a single product at retailers. The objective is to locate distribution centers in the network such that the sum of facility location, pipeline inventory, and safety stock costs is minimized. We explicitly model the relationship between the flows in the network, lead times, and safety stock levels. We use genetic algorithms to solve the model and compare their performance to that of a Lagrangian heuristic developed in earlier work. A novel chromosome representation that combines binary vectors with random keys provides solutions of similar quality to those from the Lagrangian heuristic. The model is then extended to incorporate arbitrary demand variance at the retailers. This modification destroys the structure upon which the Lagrangian heuristic is based, but is easily incorporated into the genetic algorithm. The genetic algorithm yields significantly better solutions than a greedy heuristic for this modification and has reasonable computational requirements.