Nonparametric Productivity Analysis

How can we measure and compare the relative performance of production units? If input and output variables are one dimensional, then the simplest way is to compute efficiency by calculating and comparing the ratio of output and input for each production unit. This idea is inappropriate though, when multiple inputs or multiple outputs are observed. Consider a bank, for example, with three branches A, B, and C. The branches take the number of staff as the input, and measures outputs such as the number of transactions on personal and business accounts. Assume that the following statistics are observed: Branch A: 60000 personal transactions, 50000 business transactions, 25 people on staff, Branch B: 50000 personal transactions, 25000 business transactions, 15 people on staff, Branch C: 45000 personal transactions, 15000 business transactions, 10 people on staff. We observe that Branch C performed best in terms of personal transactions per staff, whereas Branch A has the highest ratio of business transactions per staff. By contrast Branch B performed better than Branch A in terms of personal transactions per staff, and better than Branch C in terms of business transactions per staff. How can we compare these business units in a fair way? Moreover, can we possibly create a virtual branch that reflects the input/output mechanism and thus creates a scale for the real branches? Productivity analysis provides a systematic approach to these problems. We review the basic concepts of productivity analysis and two popular methods DEA and FDH, which are given in Sections 12.1 and 12.2, respectively. Sections 12.3 and 12.4 contain illustrative examples with real data.relative performance, production units, productivity analysis, Data Envelopment Analysis, DEA, Free Disposal Hull, DFH, insurance agencies, manufacturing industry

Limit Distribution of Convex-Hull Estimators of Boundaries

Given n independent and identically distributed observations in a set G with an unknown function g, called a boundary or frontier, it is desired to estimate g from the observations. The problem has several important applications including classification and cluster analysis, and is closely related to edge estimation in image reconstruction. It is particularly important in econometrics. The convex-hull estimator of a boundary or frontier is very popular in econometrics, where it is a cornerstone of a method known as `data envelope analysis´ or DEA. In this paper we give a large sample approximation of the distribution of the convex-hull estimator in the general case where p>=1. We discuss ways of using the large sample approximation to correct the bias of the convex-hull and the DEA estimators and to construct confidence intervals for the true function. --Convex-hull,free disposal hull,frontier function,data envelope analysis,productivity analysis,rate of convergence

Asymptotic distribution of conical-hull estimators of directional edges

Nonparametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are defined in terms of convex-hulls of the observed combinations of $\mathrm{inputs}\times\mathrm{outputs}$ in a sample of enterprises. The shape of the convex-hull relies on a hypothesis on the shape of the technology, defined as the boundary of the set of technically attainable points in the $\mathrm{inputs}\times\mathrm{outputs}$ space. So far, only the statistical properties of the smallest convex polyhedron enveloping the data points has been considered which corresponds to a situation where the technology presents variable returns-to-scale (VRS). This paper analyzes the case where the most common constant returns-to-scale (CRS) hypothesis is assumed. Here the DEA is defined as the smallest conical-hull with vertex at the origin enveloping the cloud of observed points. In this paper we determine the asymptotic properties of this estimator, showing that the rate of convergence is better than for the VRS estimator. We derive also its asymptotic sampling distribution with a practical way to simulate it. This allows to define a bias-corrected estimator and to build confidence intervals for the frontier. We compare in a simulated example the bias-corrected estimator with the original conical-hull estimator and show its superiority in terms of median squared error.Comment: Published in at http://dx.doi.org/10.1214/09-AOS746 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonparametric Productivity Analysis

How can we measure and compare the relative performance of production units? If input and output variables are one dimensional, then the simplest way is to compute efficiency by calculating and comparing the ratio of output and input for each production unit. This idea is inappropriate though, when multiple inputs or multiple outputs are observed. Consider a bank, for example, with three branches A, B, and C. The branches take the number of staff as the input, and measures outputs such as the number of transactions on personal and business accounts. Assume that the following statistics are observed: Branch A: 60000 personal transactions, 50000 business transactions, 25 people on staff, Branch B: 50000 personal transactions, 25000 business transactions, 15 people on staff, Branch C: 45000 personal transactions, 15000 business transactions, 10 people on staff. We observe that Branch C performed best in terms of personal transactions per staff, whereas Branch A has the highest ratio of business transactions per staff. By contrast Branch B performed better than Branch A in terms of personal transactions per staff, and better than Branch C in terms of business transactions per staff. How can we compare these business units in a fair way? Moreover, can we possibly create a virtual branch that reflects the input/output mechanism and thus creates a scale for the real branches? Productivity analysis provides a systematic approach to these problems. We review the basic concepts of productivity analysis and two popular methods DEA and FDH, which are given in Sections 12.1 and 12.2, respectively. Sections 12.3 and 12.4 contain illustrative examples with real data

Limit Distribution of Convex-Hull Estimators of Boundaries

Given n independent and identically distributed observations in a set G with an unknown function g, called a boundary or frontier, it is desired to estimate g from the observations. The problem has several important applications including classification and cluster analysis, and is closely related to edge estimation in image reconstruction. It is particularly important in econometrics. The convex-hull estimator of a boundary or frontier is very popular in econometrics, where it is a cornerstone of a method known as `data envelope analysis´ or DEA. In this paper we give a large sample approximation of the distribution of the convex-hull estimator in the general case where p>=1. We discuss ways of using the large sample approximation to correct the bias of the convex-hull and the DEA estimators and to construct confidence intervals for the true function

A Method of Calculating Motion Error in a Linear Motion Bearing Stage

We report a method of calculating the motion error of a linear motion bearing stage. The transfer function method, which exploits reaction forces of individual bearings, is effective for estimating motion errors; however, it requires the rail-form errors. This is not suitable for a linear motion bearing stage because obtaining the rail-form errors is not straightforward. In the method described here, we use the straightness errors of a bearing block to calculate the reaction forces on the bearing block. The reaction forces were compared with those of the transfer function method. Parallelism errors between two rails were considered, and the motion errors of the linear motion bearing stage were measured and compared with the results of the calculations, revealing good agreement

Properties Of Analyst Forecasts And Bond Underwriting Relationship: Evidence From Korea

Previous studies find that analysts forecast earnings more optimistically but inaccurately when they face the conflict of interest (COI). We extend this line of research by examining whether analysts’ forecasting behavior affected by the mere existence of potential COI are related with underwriting contracts.We document that analysts affiliated with security companies that become underwriters ex post issue more optimistic but less accurate forecasts for firms to issue bonds in Korea. We also find that firms to issue bonds are likely to award underwriting contracts to security companies with analysts who issue more optimistic but less accurate forecasts.  

Severe COVID-19 Illness: Risk Factors and Its Burden on Critical Care Resources

In South Korea, the first confirmed case of coronavirus 2019 (COVID-19) was detected on January 20, 2020. After a month, the number of confirmed cases surged, as community transmission occurred. The local hospitals experienced severe shortages in medical resources such as mechanical ventilators and extracorporeal membrane oxygenation (ECMO) equipment. With the medical claims data of 7,590 COVID-19 confirmed patients, this study examined how the demand for major medical resources and medications changed during the outbreak and subsequent stabilization period of COVID-19 in South Korea. We also aimed to investigate how the underlying diseases and demographic factors affect disease severity. Our findings revealed that the risk of being treated with a mechanical ventilator or ECMO (critical condition) was almost twice as high in men, and a previous history of hypertension, diabetes, and psychiatric diseases increased the risk for progressing to critical condition [Odds Ratio (95% CI), 1.60 (1.14–2.24); 1.55 (1.55–2.06); 1.73 (1.25–2.39), respectively]. Although chronic pulmonary disease did not significantly increase the risk for severity of the illness, patients with a Charlson comorbidity index score of ≥5 and those treated in an outbreak area had an increased risk of developing a critical condition [3.82 (3.82–8.15); 1.59 (1.20–2.09), respectively]. Our results may help clinicians predict the demand for medical resources during the spread of COVID-19 infection and identify patients who are likely to develop severe disease

Natural durability of some hardwoods imported into korea for deck boards against decay fungi and subterranean termite in accelerated laboratory tests

This study evaluated the natural durability of seven imported hardwoods (bangkirai, burckella, ipe, jarrah, kempas, malas, and merbau) used for deck boards against decay fungi (Fomitopsis palustris, Gloeophyllum trabeum, Trametes versicolor, and Irpex lacteus) and the subterranean termite (Reticulitermes speratus kyushuensis) in accelerated laboratory tests. Ipe, jarrah, and merbau were very durable to fungal attack, with performance comparable to ACQ-treated wood. Bangkirai, burckella, kempas, and malas were classified as durable or moderately durable, depending on the fungal species tested. All wood species except for merbau were highly resistant to termite attack. Termite resistance was similar to ACQ-treated wood. Merbau showed somewhat less than all other species but still significant termite resistance. These results indicated that selected naturally durable hardwood species could inhibit fungal and termite attacks as effectively as ACQ treatment. The natural durability of wood species tested in this study is most likely due to the biocidal extractive content of the wood