Probability of correct selection of weibull versus gamma based on livelihood ratio

This paper proposes the use of tne likelihood ratio statistic in choosing between a Neibull or gamma model, values of the probability of correct seeiection are obtained by Monte Carlo simulation. This method provides some basis for decision even when the sample size is small. The technique is applied to four sets of data from the literature.     

Identification of target clusters by using the restricted normal mixture model

This paper addresses the problem of identifying groups that satisfy the specific conditions for the means of feature variables. In this study, we refer to the identified groups as “target clusters” (TCs). To identify TCs, we propose a method based on the normal mixture model (NMM) restricted by a linear combination of means. We provide an expectation–maximization (EM) algorithm to fit the restricted NMM by using the maximum-likelihood method. The convergence property of the EM algorithm and a reasonable set of initial estimates are presented. We demonstrate the method's usefulness and validity through a simulation study and two well-known data sets. The proposed method provides several types of useful clusters, which would be difficult to achieve with conventional clustering or exploratory data analysis methods based on the ordinary NMM. A simple comparison with another target clustering approach shows that the proposed method is promising in the identification.     

Determination of the Selection Statistics and Best Significance Level in Backward Stepwise Logistic Regression

The weighted generalized estimating equation (WGEE), an extension of the generalized estimating equation (GEE) method, is a method for analyzing incomplete longitudinal data. An inappropriate specification of the working correlation structure results in the loss of efficiency of the GEE estimation. In this study, we evaluated the efficiency of WGEE estimation for incomplete longitudinal data when the working correlation structure was misspecified. As a result, we found that the efficiency of the WGEE estimation was lower when an improper working correlation structure was selected, similar to the case of the GEE method. Furthermore, we modified the criterion proposed by Gosho et al. (2011 Gosho, M., Hamada, C. and Yoshimura, I. 2011. Criterion for the selection of a working correlation structure in the generalized estimating equation approach for longitudinal balanced data. Communications in Statistics -Theory and Methods, 40: 3839–3856. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) for selecting a working correlation structure, such that the GEE and WGEE methods can be applied to incomplete longitudinal data, and we investigated the performance of the modified criterion. The results revealed that when the modified criterion was adopted, the proportion that the true correlation structure was selected was likely higher than that in the case of adopting other competing approaches.     

Canonical Correlation Analysis Using Small Number of Samples

Canonical correlation assesses the relationship between two groups of variables. Although it has been a useful tool in a wide variety of research areas, it is not well known that weaker canonical correlations require larger sample sizes to be correctly inferred. In this article, we investigate small sample bias in canonical correlation analysis and apply the jackknife bias correction to the estimation of canonical correlations. We use bootstrap samples to obtain a better confidence interval for the jackknife canonical correlation estimator.     

Mobile safety cameras: estimating casualty reductions and the demand for secondary healthcare

We consider a fully Bayesian analysis of road casualty data at 56 designated mobile safety camera sites in the Northumbria Police Force area in the UK. It is well documented that regression to the mean (RTM) can exaggerate the effectiveness of road safety measures and, since the 1980s, an empirical Bayes (EB) estimation framework has become the gold standard for separating real treatment effects from those of RTM. In this paper we suggest some diagnostics to check the assumptions underpinning the standard estimation framework. We also show that, relative to a fully Bayesian treatment, the EB method is over-optimistic when quantifying the variability of estimates of casualty frequency. Implementing a fully Bayesian analysis via Markov chain Monte Carlo also provides a more flexible and complete inferential procedure. We assess the sensitivity of estimates of treatment effectiveness, as well as the expected monetary value of prevention owing to the implementation of the safety cameras, to different model specifications, which include the estimation of trend and the construction of informative priors for some parameters.     

Multivariate EWMA Control Chart with Adaptive Sample Sizes

Standard multivariate control charts usually employ fixed sample sizes at equal sampling intervals to monitor a process. In this study, a multivariate exponential weighted moving average (MEWMA) chart with adaptive sample sizes is investigated. Performance measure of the adaptive-sample-size MEWMA chart is obtained through a Markov chain approach. The performance of the adaptive-sample-size MEWMA chart is compared with the fixed-sample-size control chart in terms of steady-state average run length for different magnitude of shifts in the process mean. It is shown that the adaptive-sample-size chart is more efficient than the fixed-sample-size MEWMA control chart in detecting shifts in the process mean.     

Economic Design of Cumulative Sum Control Charts for Monitoring a Process with Correlated Samples

The underlying assumption for the design of control charts is the measurements within a sample are independently distributed. However, there are many situations where the uncorrelation assumption may be unacceptable in practice. In this paper, the economic design of cumulative sum (CUSUM) control chart for correlated data within a sample is developed. The genetic algorithm is applied to find the optimal design parameters of the CUSUM control chart by minimizing the cost function. An illustrative example is given. A sensitivity analysis is then conducted to evaluate the effects of cost parameters, process parameters, and correlation coefficient on the economic design.     

The Design of the Multivariate Synthetic Exponentially Weighted Moving Average Control Chart

A multivariate synthetic exponentially weighted moving average (MSEWMA) control chart is presented in this study. The MSEWMA control chart consists of a multivariate exponentially weighted moving average (MEWMA) control chart and a conforming run length control chart. The average run length of the MSEWMA control chart is obtained using a Markov chain approach. From the numerical comparisons, it is shown that the MSEWMA control chart is more efficient than the multivariate synthetic T ² control chart and the MEWMA control chart for detecting shifts in the process mean vector.     

A Regression Model for the AUC of Clustered Ordinal Test Results and Working Independent Optimal Weights

We study a regression model on the area under the receiver operating characteristic curves (AUC) for clustered (or repeatedly measured) test results. To account for cluster information, we consider a weighted estimating equation for Dodd and Pepe (2003 Dodd , L. , Pepe , M. ( 2003 ). Semiparametric regression for the area under the receiver operating charateristic curve . Journal of the American Statistical Association 98 : 409 – 417 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar])'s regression model with working independence weights. We find the optimal weight in the given class of working independence weights to minimize the variance (or MSE) of regression estimators. We apply the proposed procedure to analyzing our recent experiment on diagnosing a liver disorder. In this experiment, we investigated MRI images of patients having symptoms of potential liver disorder to compare the performance of different MRI picturing methods in testing for liver disorders.