Tail density estimation for exploratory data analysis using kernel methods

It is often critical to accurately model the upper tail behaviour of a random process. Nonparametric density estimation methods are commonly implemented as exploratory data analysis techniques for this purpose and can avoid model specification biases implied by using parametric estimators. In particular, kernel-based estimators place minimal assumptions on the data, and provide improved visualisation over scatterplots and histograms. However kernel density estimators can perform poorly when estimating tail behaviour above a threshold, and can over-emphasise bumps in the density for heavy tailed data. We develop a transformation kernel density estimator which is able to handle heavy tailed and bounded data, and is robust to threshold choice. We derive closed form expressions for its asymptotic bias and variance, which demonstrate its good performance in the tail region. Finite sample performance is illustrated in numerical studies, and in an expanded analysis of the performance of global climate models.     

Rates of convergence of autocorrelation estimates for periodically correlated autoregressive Hilbertian processes

Autoregressive Hilbertian (ARH) processes are of great importance in the analysis of functional time series data and estimation of the autocorrelation operators attracts the attention of various researchers. In this paper, we study estimators of the autocorrelation operators of periodically correlated autoregressive Hilbertian processes of order one (PCARH(1)), which is an extension of ARH(1) processes. The estimation method is based on the spectral decomposition of the covariance operator and considers two main cases: known and unknown eigenvectors. We show the consistency in the mean integrated quadratic sense of the estimators of the autocorrelation operators and present upper bounds for the corresponding rates.     

Spatial prediction of crystalline defects observed in molecular dynamic simulations of plastic damage

Molecular dynamic computer simulation is an essential tool in materials science to study atomic properties of materials in extreme environments and guide development of new materials. We propose a statistical analysis to emulate simulation output with the ultimate goal of efficiently approximating the computationally intensive simulation. We compare several spatial regression approaches including conditional autoregression (CAR), discrete wavelets transform (DWT), and principle components analysis (PCA). The methods are applied to simulation of copper atoms with twin wall and dislocation loop defects, under varying tilt tension angles. We find that CAR and DWT yield accurate results but fail to capture extreme defects, yet PCA better captures defect structure.     

On convergence rate in the SLLN for maximums of moving-average sums of ALNQD random fields

In this article, we define a notion of asymptotically linear negatively quadrant dependence and establish the rate of complete convergence for maximums of moving-average sums of asymptotically linear negatively quadrant dependent random fields.     

Spatial–temporal interpolation of non methane hydrocarbon levels in Kuwait

This article handles the prediction of hourly concentrations ofnon methane hydrocarbon (NMHC) pollutants at 15 unmonitored sites in Kuwait using the data recorded from 6 monitored stations at successive time points. The trend model depends on hourly meteorological variables and seasonal effects. The stochasticcomponent of the trend model which has spatiotemporal features is modeled as autoregressive temporal process. A spatial predictive distribution for residuals of the AR model is developed for the unmonitored sites. By transforming the predicted residuals back to the original data scales, we impute Kuwait’s hourly NMHC field.     

Measuring efficiency with products,by-products and parent-offspring relations: A conditional two-stage DEA model

In the usual data envelopment analysis (DEA) setting, as pioneered by Charnes et al. (1978) [1], it is assumed that a set of decision making units (DMUs) is to be evaluated in terms of their relative efficiencies in converting a bundle of inputs into a bundle of outputs. The usual assumption in DEA is that each output is impacted by each and every member of the input set. One particular area of recent research is that relating to partial input to output impacts where the main issue addressed is that in many settings not all inputs impact all outputs. In that situation the authors view the DMU as consisting of a set of mutually exclusive subunits, with each subunit having its own unique bundle of inputs and outputs. Examined as well in this area, is the presence of multiple processes for generating sets of outputs. Missing from that earlier work is consideration of the presence of outputs in the form of by-products, giving rise to a parent-offspring phenomenon. One of the modeling complications there is that the parent assumes two different roles; as an input affecting the offspring, while at the same time being the dominant output. This gives rise to a model that we refer to as conditional two-stage. Another complication is that in the presence of multiple processes, by-products often arise out of only a subset of those processes. In the current paper we develop a DEA-type of methodology to handle partial input to output impacts in the presence of by-products.     

Commentary on Knowledge Creation and Dissemination in Operations and Supply‐Chain Management

The title of this paper might have been Knowledge Creation and Dissemination in the POM Domain . Instead, these accomplished authors (who shall be dubbed with honorable intentions as RSST) define the POM domain as Operations and Supply‐Chain Management. Thereby, they leave no doubt that the POM domain spans the entire supply chain from shovels in the mine and seeds in the ground to recycled waste that is remanufactured and sold as new (as well as refurbished) products. RSST declare that sustainability of the ecosystem cycle must be achieved (even in the face of disaster conditions) by all institutions. RSST believe that practitioners can be taught the necessary attitudes and skills by business and engineering schools. It is noteworthy that the ecosystem cycle they describe is accompanied by marketing and financial decision cycles running parallel from inception of ideas to the “end of life” closure that starts a new cycle for closed‐loop product planning. For these coexisting, interdependent, all‐encompassing systems, the RSST team leaves no doubt about the evolution of teaching and research opportunities for young POM scholars. These authors focus on the fact that everything that is not morphing is likely to become counterproductive in the not too far future. This is a critical point of view which is based on the fact that the status quo is highly vulnerable. Also, very special is the RSST warning that changes are required in the status quo which must be made without damaging the existing fabric. This non‐disruptive way of doing POM business has been remarkably successful for the cohesion of the field over the past 25 years. There is agreement that it is great to shake things up without tearing those things apart. All of this leads to the conclusion that the advice of these authors (RSST) is correct and valuable. Debate and disputation of these points is encouraged and expected by the RSST team.     

Experimental Results Indicating Lattice‐Dependent Policies May Be Optimal for General Assemble‐To‐Order Systems

We consider an assemble‐to‐order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite‐horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice‐dependent base‐stock and lattice‐dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M‐system). In this study, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state‐dependent base‐stock and state‐dependent rationing (SBSR) policy, and a fixed base‐stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.