One-Class Classification-Based Control Charts for Monitoring Autocorrelated Multivariate Processes

In recent years, statistical process control (SPC) of multivariate and autocorrelated processes has received a great deal of attention. Modern manufacturing/service systems with more advanced technology and higher production rates can generate complex processes in which consecutive observations are dependent and each variable is correlated. These processes obviously violate the assumption of the independence of each observation that underlies traditional SPC and thus deteriorate the performance of its traditional tools. The popular way to address this issue is to monitor the residuals—the difference between the actual value and the fitted value—with the traditional SPC approach. However, this residuals-based approach requires two steps: (1) finding the residuals; and (2) monitoring the process. Also, an accurate prediction model is necessary to obtain the uncorrelated residuals. Furthermore, these residuals are not the original values of the observations and consequently may have lost some useful information about the targeted process. The main purpose of this article is to examine the feasibility of using one-class classification-based control charts to handle multivariate and autocorrelated processes. The article uses simulated data to present an analysis and comparison of one-class classification-based control charts and the traditional Hotelling's T ² chart.     

Estimation of the derivative of a density and related functions

Let Y₁,…,Y _n, (Y₁ <Y₂<…<Y _n) be the order statistics of a random sample from a distribution F with density f on the realline. This paper gives a class of estimators of the derivativef'(x) of the density f at points x for which f has

a continuoussecond derivative. These estimators are based on spacings inthe order statistics Y_j+kn -y _j j = 1,…,n-k_n,k_n<n.     

On the problem of selecting good populations

The problem of selecting good populations out of k normal populations is considered in a Bayesian framework under exchangeable normal priors and additive loss functions. Some basic approximations to the Bayes rules are discussed. These approximations suggest that some well-known classical rules are "approximate" Bayes rules. Especially, it is shown that Gupta-type rules are extended Bayes with respect to a family of the exchangeable normal priors for any bounded and additive loss function. Furthermore, for a simple loss function, the results of a Monte Carlo comparison of Gupta-type rules and Seal-type rules are presented. They indicate that, in general, Gupta-type rules perform better than Seal-type rules     

Admissible estimation in an one parameter nonregular family of absolutely continuous distributions

Consider the problem of estimating under squared error loss an arbitrarily positive, strictly increasing or decreasing parametric function based on a sample of size n in an one parameter nonregular family of absolutly continuous distributions with both endpoints of the support depending on a single parameter. We first provide sufficient conditions for the admissibility of generalized Bayes estimators with respect to some specific priors and then treat several examples which illustrate the admissibility of best invariant estimators in some location or scale parameter problems.     

A note on some negative dependence notions

A random vector X = (X ₁,…,X _n ) is negatively associated if and only if for every pair of partitions X ₁ = (X _π(1),…,X _π(k)), X ₂ = (X _π(k+1),…,X _π(n)) of X , P( X ₁ ? A, X ₂ ? B) ≤ P( X ₁ ? A)P( X ₂ ? B) whenever A and B are open upper sets and π is any permutation of {1,…,n}. In this paper, we develop some of concepts of negative dependence, which are weaker than negative association but stronger than negative orthant dependence by requiring the above inequality to hold only for some upper sets A and B and applying the arguments in Shaked.     

Tests for detecting overdispersion in poisson models

Collings and Margolin(1985) developed a locally most powerful unbiased test for detecting negative binomial departures from a Poisson model, when the variance is a quadratic function of the mean. Kim and Park(1992) developed a locally most powerful unbiased test, when the variance is a linear function of the mean. It is found that a different mean-variance structure of a negative binomial derives a different locally optimal test statistic.

In this paper Collings and Margolin's and Kim and Park's results are unified and extended by developing a test for overdispersion in Poisson model against Katz family of distributions, Our setup has two extensions: First, Katz family of distributions is employed as an extension of the negative binomial distribution. Second, the mean-variance structure of the mixed Poisson model is given by σ² = μ+cμ^r for arbitrary but fixed r. We derive a local score test for testing H₀ : c = 0. Superiority of a new test is proved by the asymtotic relative efficiency as well as the simulation study.     

Asymptotic test of mixture model and its applications to QTL interval mapping

Quantitative trait loci (QTL) mapping has been a standard means in identifying genetic regions harboring potential genes underlying complex traits. Likelihood ratio test (LRT) has been commonly applied to assess the significance of a genetic locus in a mixture model content. Given the time constraint in commonly used permutation tests to assess the significance of LRT in QTL mapping, we study the behavior of the LRT statistic in mixture model when the proportions of the distributions are unknown. We found that the asymptotic null distribution is stationary Gaussian process after suitable transformation. The result can be applied to one-parameter exponential family mixture model. Under certain condition, such as in a backcross mapping model, the tail probability of the supremum of the process is calculated and the threshold values can be determined by solving the distribution function. Simulation studies were performed to evaluate the asymptotic results.     

The Impact of Age and Health on Vehicle Choices among Elders

We examine older Americans’ choice of vehicle types and the impact of age and health status on this choice. Using the 1998 and 2000 Health and Retirement Study (HRS) and the 2001 HRS Consumption and Activities Mail Survey (CAMS), we estimate a multinomial logit model of older Americans’ choice of vehicle types. We find that both age and health status influence the type of vehicle purchased or leased. Compared to Americans aged 50–59, those aged 70 or older prefer passenger cars to trucks and sport utility vehicles (SUVs). We also find that elders with health problems are more likely to prefer SUVs to passenger cars than those without health problems.

Assessing the risk factors for suicidal thoughts at a nontraditional commuter school

The sample of students completing the National College Health Assessment (NCHA) Survey at the University of Utah differs from the national reference group for the NCHA 2003 in age, employment, residence, and marital status. The purpose of this study is to determine if the defining characteristics of a commuter school increase the risk for suicidal thoughts. During the fall semester of 2004, the University of Utah implemented a randomized electronic survey assessing the student body's health status in several areas. The authors compared 88 respondents who endorsed seriously considered suicide in the previous 12 months were with the remaining 954 respondents to identify discriminating variables. Those students who seriously considered suicide more likely lived off campus, indicated they were emotionally abused, were in only fair health, experienced being assaulted, experienced unwanted sexual touching, or were not heterosexual. Students who were employed were significantly less likely to consider suicide.