Optimal design of the adaptive exponentially weighted moving average control chart over a range of mean shifts

The adaptive exponentially weighted moving average (AEWMA) control chart is a smooth combination of the Shewhart and exponentially weighted moving average (EWMA) control charts. This chart was proposed by Cappizzi and Masarotto (2003) to achieve a reasonable performance for both small and large shifts. Cappizzi and Masarotto (2003) used a pair of shifts in designing their control chart. In this study, however, the process mean shift is considered as a random variable with a certain probability distribution and the AEWMA control chart is optimized for a wide range of mean shifts according to that probability distribution and not just for a pair of shifts. Using the Markov chain technique, the results show that the new optimization design can improve the performance of the AEWMA control chart from an overall point of view relative to the various designs presented by Cappizzi and Masarotto (2003). Optimal design parameters that achieve the desired in-control average run length (ARL) are computed in several cases and formulas used to find approximately their values are given. Using these formulas, the practitioner can compute the optimal design parameters corresponding to any desired in-control ARL without the need to apply the optimization procedure. The results obtained by these formulas are very promising and would particularly facilitate the design of the AEWMA control chart for any in-control ARL value.     

Periodic integer-valued bilinear time series model

This paper deals with the study of some probabilistic and statistical properties of a periodic integer-valued diagonal bilinear model. The existence of a periodically strict stationary integer-valued process is shown. Sufficient conditions for the periodically stationary, both in the first and second orders, are established. The closed-forms of the mean and the second moment are obtained. The closed-form of the periodic autocovariance function is established. The Yule–Walker estimations of the underlying parameters are obtained. A simulation study is provided.     

The local geographies of welfare in Tunisia: Does neighbourhood matter?*

Amara M, Ayadi M. The local geographies of welfare in Tunisia: Does neighbourhood matter? The aim of this article is to show that spatial analysis techniques outperform non‐spatial statistical counterparts for understanding the geographic determinants of welfare and poverty in Tunisia. First, an Exploratory Spatial Data Analysis, based on a Geographical Information System, was conducted to visualise the local spatial structure of welfare. Second, a spatial autoregressive (SAR) model and a geographically weighted regression (GWR) model, respectively, were used to deal with both spatial autocorrelations and unobserved spatial heterogeneity of households' behaviours. Spatial and non‐spatial models were compared according to their predictive performances. Results of this case study confirm that SAR and GWR spatial models are preferable to the traditional non‐spatial regression model and that they give a better approximation of the Tunisian poverty map.     

Sparse conformal predictors

Conformal predictors, introduced by Vovk et al. (Algorithmic Learning in a Random World, Springer, New York, 2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. We propose a novel method for constructing prediction intervals for the response variable in multivariate linear models. The main emphasis is on sparse linear models, where only few of the covariates have significant influence on the response variable even if the total number of covariates is very large. Our approach is based on combining the principle of conformal prediction with the ℓ ₁ penalized least squares estimator (LASSO). The resulting confidence set depends on a parameter ε>0 and has a coverage probability larger than or equal to 1−ε. The numerical experiments reported in the paper show that the length of the confidence set is small. Furthermore, as a by-product of the proposed approach, we provide a data-driven procedure for choosing the LASSO penalty. The selection power of the method is illustrated on simulated and real data.     

Maximum likelihood approach to vote aggregation with variable probabilities

The Condorcet-Kemeny-Young statistical approach to vote aggregation is based on the assumption that voters have the same probability of comparing correctly two alternatives and that this probability is the same for any pair of alternatives. We relax the second part of this assumption by letting the probability of comparing correctly two alternatives be increasing with the distance between two alternatives in the allegedly true ranking. This leads to a rule in which the majority in favor of one alternative against another one is given a larger weight the larger the distance between the two alternatives in the true ranking, i.e., the larger the probability that the voters compare them correctly. This rule is not Condorcet consistent and does not satisfy local independence of irrelevant alternatives. Yet, it is anonymous, neutral, and paretian. It also appears that its performance in selecting the alternative most likely to be the best improves with the rate at which the probability increases.We would like to thank Michel Le Breton for his encouragement to examine this question and for his comments, as well as Philippe De Donder, Jean-Yves Duclos, Stephen Gordon, Cyril Téjédo and an anonymous referee for their comments.     

Psychology in the Arab World: Past, Present, and Future

In this article, we present a broad-based view of psychology in the Arab countries. We begin by casting light on the relevant contributions by ancient Arab scholars in the Middle Ages. Given that systematic scientific investigation of this legacy has been minuscule, we argue that in the future, scholars seeking to provide a more balanced and comprehensive history of Arab psychology should reanalyze these works. We point out that in the early decades of the modern twentieth century, Western psychology was introduced in the Arab countries, especially in Egypt—the gateway through which such psychology was introduced and practiced. By the early 1960s, a number of universities had been established in some Arab countries, and Egyptian academicians, including psychologists, were invited to perform teaching, research, and administration tasks. Their legacy was a discipline bearing most of the strengths and weaknesses of Egyptian psychology, although in spite of such commonalties, there exist also some interesting differences characterizing psychology in the various Arab countries. The final section of the article summarizes some key aspects endemic to psychology in the Arab countries.     

Order statistics from non-identical right-truncated Lomax random variables with applications

In this paper, we derive some recurrence relations for the single and the product moments of order statistics from n independent and non-identically distributed Lomax and right-truncated Lomax random variables. These recurrence relations are simple in nature and could be used systematically in order to compute all the single and product moments of all order statistics in a simple recursive manner. The results for order statistics from the multiple-outlier model (with a slippage of p observations) are deduced as special cases. We then apply these results by examining the robustness of censored BLUE's to the presence of multiple outliers. Received: November 30, 1998; revised version: March 8, 2000     

Modeling longitudinal count data with dropouts

This paper explores the utility of different approaches for modeling longitudinal count data with dropouts arising from a clinical study for the treatment of actinic keratosis lesions on the face and balding scalp. A feature of these data is that as the disease for subjects on the active arm improves their data show larger dispersion compared with those on the vehicle, exhibiting an over‐dispersion relative to the Poisson distribution. After fitting the marginal (or population averaged) model using the generalized estimating equation (GEE), we note that inferences from such a model might be biased as dropouts are treatment related. Then, we consider using a weighted GEE (WGEE) where each subject's contribution to the analysis is weighted inversely by the subject's probability of dropout. Based on the model findings, we argue that the WGEE might not address the concerns about the impact of dropouts on the efficacy findings when dropouts are treatment related. As an alternative, we consider likelihood‐based inference where random effects are added to the model to allow for heterogeneity across subjects. Finally, we consider a transition model where, unlike the previous approaches that model the log‐link function of the mean response, we model the subject's actual lesion counts. This model is an extension of the Poisson autoregressive model of order 1, where the autoregressive parameter is taken to be a function of treatment as well as other covariates to induce different dispersions and correlations for the two treatment arms. We conclude with a discussion about model selection. Published in 2009 by John Wiley & Sons, Ltd.     

Detection of outliers in simple circular regression models using the mean circular error statistic

The investigation on the identification of outliers in linear regression models can be extended to those for circular regression case. In this paper, we propose a new numerical statistic called mean circular error to identify possible outliers in circular regression models by using a row deletion approach. Through intensive simulation studies, the cut-off points of the statistic are obtained and its power of performance investigated. It is found that the performance improves as the concentration parameter of circular residuals becomes larger or the sample size becomes smaller. As an illustration, the statistic is applied to a wind direction data set.