Non-parametric estimation of the conditional mode

The problem of estimating the mode of a conditional probability density function is considered. It is shown that under some regularity conditions the estimate of the conditional mode obtained by maximizing a kernel estimate of the conditional probability density function is strongly consistent and asymptotically normally distributed.     

Bayesian prediction of waiting times in stochastic models

The authors show how saddlepoint techniques lead to highly accurate approximations for Bayesian predictive densities and cumulative distribution functions in stochastic model settings where the prior is tractable, but not necessarily the likelihood or the predictand distribution. They consider more specifically models involving predictions associated with waiting times for semi‐Markov processes whose distributions are indexed by an unknown parameter θ. Bayesian prediction for such processes when they are not stationary is also addressed and the inverse‐Gaussian based saddlepoint approximation of Wood, Booth & Butler (1993) is shown to accurately deal with the nonstationarity whereas the normal‐based Lugannani & Rice (1980) approximation cannot, Their methods are illustrated by predicting various waiting times associated with M/M/q and M/G/1 queues. They also discuss modifications to the matrix renewal theory needed for computing the moment generating functions that are used in the saddlepoint methods.     

Copula-based regression models: A survey

In this review paper we collect several results about copula-based models, especially concerning regression models, by focusing on some insurance applications.     

A new estimation method for Weibull-type tails based on the mean excess function

Studying the right tail of a distribution, one can classify the distributions into three classes based on the extreme value index γ$\gamma$. The class γ>0$\gamma >0$ corresponds to Pareto-type or heavy tailed distributions, while γ<0$\gamma <0$ indicates that the underlying distribution has a finite endpoint. The Weibull-type distributions form an important subgroup within the Gumbel class with γ=0$\gamma =0$. The tail behaviour can then be specified using the Weibull tail index. Classical estimators of this index show severe bias. In this paper we present a new estimation approach based on the mean excess function, which exhibits improved bias and mean squared error. The asserted properties are supported by simulation experiments and asymptotic results. Illustrations with real life data sets are provided.     

Improving Risk Management: From Lame Excuses to Principled Practice

The three classic pillars of risk analysis are risk assessment (how big is the risk and how sure can we be?), risk management (what shall we do about it?), and risk communication (what shall we say about it, to whom, when, and how?). We propose two complements as important parts of these three bases: risk attribution (who or what addressable conditions actually caused an accident or loss?) and learning from experience about risk reduction (what works, and how well?). Failures in complex systems usually evoke blame, often with insufficient attention to root causes of failure, including some aspects of the situation, design decisions, or social norms and culture. Focusing on blame, however, can inhibit effective learning, instead eliciting excuses to deflect attention and perceived culpability. Productive understanding of what went wrong, and how to do better, thus requires moving past recrimination and excuses. This article identifies common blame‐shifting “lame excuses” for poor risk management. These generally contribute little to effective improvements and may leave real risks and preventable causes unaddressed. We propose principles from risk and decision sciences and organizational design to improve results. These start with organizational leadership. More specifically, they include: deliberate testing and learning—especially from near‐misses and accident precursors; careful causal analysis of accidents; risk quantification; candid expression of uncertainties about costs and benefits of risk‐reduction options; optimization of tradeoffs between gathering additional information and immediate action; promotion of safety culture; and mindful allocation of people, responsibilities, and resources to reduce risks. We propose that these principles provide sound foundations for improving successful risk management.     

Setting tolerance limits for statistical project control using earned value management

Project control has been a research topic since decades that attracts both academics and practitioners. Project control systems indicate the direction of change in preliminary planning variables compared with actual performance. In case their current project performance deviates from the planned performance, a warning is indicated by the system in order to take corrective actions.Earned value management/earned schedule (EVM/ES) systems have played a central role in project control, and provide straightforward key performance metrics that measure the deviations between planned and actual performance in terms of time and cost. In this paper, a new statistical project control procedure sets tolerance limits to improve the discriminative power between progress situations that are either statistically likely or less likely to occur under the project baseline schedule. In this research, the tolerance limits are derived from subjective estimates for the activity durations of the project. Using the existing and commonly known EVM/ES metrics, the resulting project control charts will have an improved ability to trigger actions when variation in a project׳s progress exceeds certain predefined thresholdsA computational experiment has been set up to test the ability of these statistical project control charts to discriminate between variations that are either acceptable or unacceptable in the duration of the individual activities. The computational experiments compare the use of statistical tolerance limits with traditional earned value management thresholds and validate their power to report warning signals when projects tend to deviate significantly from the baseline schedule.     

Joint product assortment,inventory and price optimization to attract loyal and non-loyal customers

In this paper, we analyze the emerging retail practice of carrying a combined product assortment consisting of both regular “standard” products and more fashionable and short-lived “special” products. The purpose of this practice is to increase store traffic by attracting heterogeneous classes of customers, which drives up sales of standard products due to the potential cross-selling effect. Customers who are primarily attracted by special products will also buy some standard products. In this context, we analyze three decisions that are crucial for a retailer׳s commercial success: the product assortment, the inventory levels and the pricing. We propose an optimization model and an iterative heuristic to analyze the trade-offs between the combined product assortment, the inventory level and the price per product when there is limited shelf space. Using numerical experiments, we show that our heuristic can be trusted and that its accuracy improves when the number of products increases. Our findings indicate that to attract more customers for standard products, a retailer may benefit from carrying low priced special products which, if considered in isolation, would be non-profitable. As the cross-selling effect decreases, a retailer should focus more on the standard assortment by increasing its size and decreasing the prices. However, introducing special products and ignoring the cross-selling effect may decrease a retailer׳s profitability. We show that the introduction of special products involves more than just choosing the right specials for non-loyal customers but impacts the global assortment planning, the standard products and the products pricing.     

An Integrated Risk Assessment Model of Township‐Scaled Land Subsidence Based on an Evidential Reasoning Algorithm and Fuzzy Set Theory

Land subsidence risk assessment (LSRA) is a multi‐attribute decision analysis (MADA) problem and is often characterized by both quantitative and qualitative attributes with various types of uncertainty. Therefore, the problem needs to be modeled and analyzed using methods that can handle uncertainty. In this article, we propose an integrated assessment model based on the evidential reasoning (ER) algorithm and fuzzy set theory. The assessment model is structured as a hierarchical framework that regards land subsidence risk as a composite of two key factors: hazard and vulnerability. These factors can be described by a set of basic indicators defined by assessment grades with attributes for transforming both numerical data and subjective judgments into a belief structure. The factor‐level attributes of hazard and vulnerability are combined using the ER algorithm, which is based on the information from a belief structure calculated by the Dempster‐Shafer (D‐S) theory, and a distributed fuzzy belief structure calculated by fuzzy set theory. The results from the combined algorithms yield distributed assessment grade matrices. The application of the model to the Xixi‐Chengnan area, China, illustrates its usefulness and validity for LSRA. The model utilizes a combination of all types of evidence, including all assessment information—quantitative or qualitative, complete or incomplete, and precise or imprecise—to provide assessment grades that define risk assessment on the basis of hazard and vulnerability. The results will enable risk managers to apply different risk prevention measures and mitigation planning based on the calculated risk states.