Model Assisted Statistics and Applications

In applications of multiple regression, one of the most common goals is to measure the relative importance of each predictor variable. If the predictors are uncorrelated, quantification of relative importance is simple and unique. However, in practice, predictor variables are typically correlated and there is no unique measure of a predictor variable’s relative importance. Using a transformation to orthogonality, new measures are constructed for evaluating the contribution of individual variables to a regression sum of squares. The transformation yields an orthogonal approximation of the columns of the predictor scores matrix and it maximizes the sum of the covariances between the cross-product of individual regressors and the response variable and the cross-product of the transformed orthogonal regressors and the response variable. The new measures are compared with three previously proposed measures through examples and the properties of the measures are examined.

We introduce a notion of a probability space of regression models and discuss its applications to financial time series. The probability space of regression models ℒ = ( ℳ , ℘ ) consists of a set of regression models ℳ and a probability measure ℘ , which is based on the model “quality”, i.e. its ability to “fit” into historical data and to forecast the future values of the target variable. The set of regression models ℳ is assembled by selecting various combinations of input variables with different lags, transformations, etc., and varying historical data sets that are used for model building and validation. It is assumed that the model set ℳ is “complete” in the sense that it exhausts all the “meaningful” regression models that are possible to be built given available historical data and independent variables. Each model M from the set ℳ yields a scenario y ⁢ ( t ; m ) for the target variable y , and thus the probability space of regression models ℒ = ( ℳ , ℘ ) allows one to build a probability distribution for Y ⁢ ( t ) for each projection time t . We demonstrate how those distributions can be used to estimate risk capital reserves required by the regulators for large U.S. banks for credit and operational risks under the macroeconomic scenarios provided by the Federal Reserve Bank (FRB) for the Comprehensive Capital Analysis and Review (CCAR) stress testing.

Theft-Related Shrink (TRS) is a common problem in the retail industry and researchers and retail managers have proposed various solutions to reduce it. Most of the solutions proposed and discussed in literature are in the domains of retail surveillance systems and structures, surveillance technology installation and its upgradation, economic incentives to employees, training and development of employees, and recruitment and hiring full time employees. A few quantitative studies have reported the negative relationship between the retail floor employee density (ED) and TRS. These studies have indicated that an increase in ED leads to reduction in TRS. However, there is a gap in the literature related to optimizing employee density to reduce TRS, as this idea has not been explored and presented in the extant literature. In this paper, a formula is developed and presented for optimal employee density (OED) to reduce the sum total of TRS and employees cost (EC) to the minimum. The formula could be useful to researchers, retail store managers, and human resource professionals in the retail industry to assess the number of employees required to minimize the sum total of EC and TRS and then accordingly plan the employee recruitment and hiring process.

Kanban, which is an agile process methodology as well as a means to implement lean principles, has been growing as a project management framework across a range of domains, including manufacturing, software development and data science. This paper explores, for teams using Kanban, the ability to predict low team performance. The prediction is based on an analytical model that uses specific project metrics that can be collected via the team’s visual Kanban board. Specifically, data from 80 teams was used to build and test machine learning models that predict teams at risk for delivering low quality results. The model developed was significantly better than the baseline situation of thinking that all teams were at risk. While this analysis was done within a data science project context, the results are likely applicable across a range of information system projects.

Composite materials destruction as a “Birth and Death” process of defects with chemical corrosion is discussed. The problem is closely connected with durability of materials in case of their long-term usage in corrosive environment. The statistical concept of the “weakest link” helps to consider a model of completely elastic continuous medium with a layer of small thickness extending to the maximum compression, and dissolution product is a Bingham viscous-plastic liquid filling up the layer. The equation for mathematical expectation of destruction process with continuous time and discrete but limited number of events enables us to estimate a number of defects in accordance with the energy parameters and the entire ideal elastic body, and the time to eventual fracture. One of the possible results of the random of “Birth and Death” process of defects is a total loss of medium strength. Non-destructive methods of strength control by monitoring material conductivity and spectrum of random signals upon the process of “Birth and Death” of defects are suggested.

Modern approaches to simulation, involving Monte Carlo methods and randomized procedures of decision-making, are usually dated back to the mid-20-th century and the arrival of the computer era. Deeper history goes back to the 19-th and even 18-th centuries and involves such devices as Galton’s board and Buffon’s needle. However, one can argue that long before the invention of computers, older devices such as dice and their predecessors have been effectively used for games and divination. The idea of this paper is to review the use of ancient randomizing devices to trace the history of simulation and random rules of decision-making. Special attention will be paid to some contemporary cultures, which have preserved some unique elements of their ancient history: native cultures of the Americas, the Celtic civilizations of Ireland and Scotland, and the indigenous peoples of Northern and Central Asia (Altai and Siberia).