The information matrix test in the linear regression with ARMA errors

Summary The paper shows that the informaton matrix test presented by White (1982) decomposes into the sum of quadratic forms in the case of a linear model with ARMA errors. By extending previous results, which analysed the information matrix test in the presence of serial correlation, the test allows detection of additional sources of misspecification.     

Selection of resilient supply portfolio under disruption risks

This paper deals with the optimal selection and protection of part suppliers and order quantity allocation in a supply chain with disruption risks. The protection decisions include the selection of suppliers to be protected against disruptions and the allocation of emergency inventory of parts to be pre-positioned at the protected suppliers. The decision maker needs to decide which supplier to select for parts delivery and how to allocate orders quantity among the selected suppliers, and which of the selected suppliers to protect against disruptions and how to allocate emergency inventory among the protected suppliers. The problem objective is to achieve a minimum cost of suppliers protection, emergency inventory pre-positioning, parts ordering, purchasing, transportation and shortage and to mitigate the impact of disruption risks by minimizing the potential worst-case cost. As a result a resilient supply portfolio is identified with protected suppliers capable of supplying parts in the face of disruption events. A mixed integer programming approach is proposed to determine risk-neutral, risk-averse or mean-risk supply portfolios, with conditional value-at-risk applied to control the risk of worst-case cost. Numerical examples are presented and some computational results are reported.     

Performance of weather-conditional rebates under different risk preferences

Retailers who sell seasonal products often face challenges in demand management due to weather uncertainty. In many cases, they make their ordering and pricing decisions prior to the regular selling season but the vast majority of sales do not occur until after the season starts, during which unfavorable weather conditions may result in high monetary losses. To protect against such adverse financial outcomes, retailers may offer weather-linked promotions such as weather rebates and induce customers to make early purchases. Specifically, weather-conditional rebates are incentives offered in an advance promotional period to be paid to the early buyers if the weather state in the regular season is unfavorable. In the presence of seasonal weather uncertainty, risk attitudes of retailers and buyers may play an important role on the effectiveness of these promotions. In this paper, we analyze the performance of weather-conditional rebates by explicitly considering the impact of different risk behaviors. First, we study the case in which the retailer and customers are risk-neutral and show that the weather-conditional rebates are effective in increasing the retailer's profits. Under the assumption of the retailer's risk-neutrality, we conduct a simulation study to investigate the impact of customers' alternative early-purchase behaviors on the performance of the rebate program. Next, we consider a risk-averse retailer. We model the retailer's risk aversion primarily in the mean–variance framework and find that the rebate program can be designed to increase the mean profit and reduce the profit variance simultaneously. Furthermore, by combining the rebate program with a financial instrument such as binary weather options, the retailer can obtain greater benefits from weather-conditional rebates.     

Chain graph models: topological sorting of meta-arrows and efficient construction of $${\mathcal{B}}$$ -essential graphs

Essential graphs and largest chain graphs are well-established graphical representations of equivalence classes of directed acyclic graphs and chain graphs respectively, especially useful in the context of model selection. Recently, the notion of a labelled block ordering of vertices was introduced as a flexible tool for specifying subfamilies of chain graphs. In particular, both the family of directed acyclic graphs and the family of “unconstrained” chain graphs can be specified in this way, for the appropriate choice of . The family of chain graphs identified by a labelled block ordering of vertices is partitioned into equivalence classes each represented by means of a -essential graph. In this paper, we introduce a topological ordering of meta-arrows and use this concept to devise an efficient procedure for the construction of -essential graphs. In this way we also provide an efficient procedure for the construction of both largest chain graphs and essential graphs. The key feature of the proposed procedure is that every meta-arrow needs to be processed only once.     

Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type-II censoring

In reliability analysis, accelerated life-testing allows for gradual increment of stress levels on test units during an experiment. In a special class of accelerated life tests known as step-stress tests, the stress levels increase discretely at pre-fixed time points, and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. In this article, we consider the simple step-stress model under Type-II censoring when the lifetime distributions of the different risk factors are independently exponentially distributed. Under this setup, we derive the maximum likelihood estimators (MLEs) of the unknown mean parameters of the different causes under the assumption of a cumulative exposure model. The exact distributions of the MLEs of the parameters are then derived through the use of conditional moment generating functions. Using these exact distributions as well as the asymptotic distributions and the parametric bootstrap method, we discuss the construction of confidence intervals for the parameters and assess their performance through Monte Carlo simulations. Finally, we illustrate the methods of inference discussed here with an example.     

Monte carlo evidence on the robustness of conditional moment tests in tobit and probit models

This paper numerically examines the size robustness of various conditional moment tests in misspecified tobit and probit models. The misspecifications considered include the incorrect exclusion of regressors, ignored heteroskedasticity and false distributional assumptions. An important feature of the experimental design is that it is based on an existing empirical study and is more realistic than many simulation studies. The tests are seen to have mixed performance depending on both the original null hypothesis being tested and type of misspecification encountered.     

Approximate Likelihoods for Generalized Linear Errors-in-variables Models

When measurement error is present in covariates, it is well known that naïvely fitting a generalized linear model results in inconsistent inferences. Several methods have been proposed to adjust for measurement error without making undue distributional assumptions about the unobserved true covariates. Stefanski and Carroll focused on an unbiased estimating function rather than a likelihood approach. Their estimating function, known as the conditional score, exists for logistic regression models but has two problems: a poorly behaved Wald test and multiple solutions. They suggested a heuristic procedure to identify the best solution that works well in practice but has little theoretical support compared with maximum likelihood estimation. To help to resolve these problems, we propose a conditional quasi-likelihood to accompany the conditional score that provides an alternative to Wald's test and successfully identifies the consistent solution in large samples.     

Does work during childhood affect the health of Guatemalan adults?

The diversity of potential relationships between child labor and health makes the empirical disentanglement of the causal relationship a difficult exercise. This paper examines the long run impact of child labour on health by controlling for unobserved household specific characteristics. In order to control for the unobserved households specific effect, we estimate a conditional fixed effect model using data on siblings constructed from the Guatemalan National Survey of Living Condition. The estimation results reinforce the conventional wisdom that child labor is harmful for health in the long run. The results can be interpreted as a lower bound of the true impact since healthier children are most likely to offer themselves for employment and to be appointed. The views expressed in this paper are those of the authors and do not necessarily represent those of IMF and IMF policy.     

Measuring the complexity of generalized linear hierarchical models

Measuring a statistical model's complexity is important for model criticism and comparison. However, it is unclear how to do this for hierarchical models due to uncertainty about how to count the random effects. The authors develop a complexity measure for generalized linear hierarchical models based on linear model theory. They demonstrate the new measure for binomial and Poisson observables modeled using various hierarchical structures, including a longitudinal model and an areal‐data model having both spatial clustering and pure heterogeneity random effects. They compare their new measure to a Bayesian index of model complexity, the effective number p_D of parameters (Spiegelhalter, Best, Carlin & van der Linde 2002); the comparisons are made in the binomial and Poisson cases via simulation and two real data examples. The two measures are usually close, but differ markedly in some instances where p_D is arguably inappropriate. Finally, the authors show how the new measure can be used to approach the difficult task of specifying prior distributions for variance components, and in the process cast further doubt on the commonly‐used vague inverse gamma prior.     

Estimation and simulation of conditional hazard function in the quasi-associated framework when the observations are linked via a functional single-index structure

We consider the estimation of the conditional hazard function of a scalar response variable Y given a Hilbertian random variable X when the observations are linked via a single-index structure in the quasi-associated framework. We establish the pointwise almost complete convergence and the uniform almost complete convergence (with the rate) of the estimate of this model. A simulation is given to illustrate the good behavior in the practice of our methodology.