Smoothing techniques via the bezier curve

Although the Bezier curve is very popular in the area of computational graphics it has rarely been used by statisticians. In this paper we develop methods and techniques for use of the Bezier curve in estimation of density and regression function. Also, asymptotic mean integrated square error for both estimators are derived. Comparisons with kernel estimator are conducted using simulation.     

Individual Disaster Assistance For Socially Vulnerable People: Lessons Learned From the Pohang Earthquake in the Republic of Korea

The Republic of Korea has been considered to be relatively safe from earthquake hazards because of the geological location of the Korean Peninsula, which has a low level of intraplate seismic activity. However, an earthquake with a moment magnitude of 5.4 struck the city of Pohang on November 15, 2017, causing 90 casualties and 52 million USD in property losses. During the recovery process after the earthquake, the Korean government provided individual disaster assistance to victims who reported their damages. However, the government disaster assistance could have been unfairly distributed among the socially vulnerable victims who essentially relied on that assistance. This study identifies whether the government disaster assistance was fairly distributed to socially vulnerable victims using a statistical model based on the data from the Pohang earthquake that occurred in 2017 in Korea. A conceptual model was constructed using a structural equation model (SEM) of three factors—social vulnerability, physical vulnerability, and the amount paid out in individual disaster assistance. Furthermore, interviews with and a survey of the victims were conducted to verify the problems identified by the conceptual model. This study found that socially vulnerable victims were less likely to take advantage of the government disaster assistance program.     

Lambda number for the direct product of some family of graphs

An L(2, 1)-labeling for a graph \(G=(V,E)\) is a function f on V such that \(|f(u)-f(v)|\ge 2\) if u and v are adjacent and f(u) and f(v) are distinct if u and v are vertices of distance two. The L(2, 1)-labeling number, or the lambda number \(\lambda (G)\), for G is the minimum span over all L(2, 1)-labelings of G. When \(P_{m}\times C_{n}\) is the direct product of a path \(P_m\) and a cycle \(C_n\), Jha et al. (Discret Appl Math 145:317–325, 2005) computed the lambda number of \(P_{m}\times C_{n}\) for \(n\ge 3\) and \(m=4,5\). They also showed that when \(m\ge 6\) and \(n\ge 7\), \(\lambda (P_{m}\times C_{n})=6\) if and only if n is the multiple of 7 and conjectured that it is 7 if otherwise. They also showed that \(\lambda (C_{7i}\times C_{7j})=6\) for some i, j. In this paper, we show that when \(m\ge 6\) and \(n\ge 3\), \(\lambda (P_m\times C_n)=7\) if and only if n is not a multiple of 7. Consequently the conjecture is proved. Here we also provide the conditions on m and n such that \(\lambda (C_m\times C_n)\le 7\).     

Alternative sensitivity analyses for regression estimates of treatment effects to unobserved confounding in binary and survival data

Statistical Methods & Applications - Estimates of treatment effects in non-experimental studies are subject to bias owing to unobserved confounding. It is desirable to assess the sensitivity of...