scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Runs and Scans With Applications

01 Dec 2002-Journal of the American Statistical Association (Taylor & Francis)-Vol. 97, Iss: 460, pp 1205-1205
TL;DR: This text is a revision of the book by Arnold, Costillo, and Sarabia (1992), but with much more depth than the original, and comprises a lively overview of conditionally speciŽ ed models of the conditional distribution.
Abstract: of the conditional distribution speciŽ cations. Chapters 8 and 10 extend these methods from two to more dimensions. Chapter 9 investigates estimation in conditionally speciŽ ed models. Chapter 11 considers models speciŽ ed by conditioning on events speciŽ ed by one variable exceeding a value rather than equaling a value, and Chapter 12 considers models for extreme-value data. Chapter 13 extends conditional speciŽ cation to Bayesian analysis. Chapter 14 describes the related simultaneous-equation models, and Chapter 15 ties in some additional topics. An appendix describes methods of simulation from conditionally speciŽ ed models. Chapters 1–4, plus Chapters 9 and 13, comprise a lively overview of conditionally speciŽ ed models. The remainder of the text constitutes a detailed catalog of results speciŽ c to different conditional distributions. Although this catalog is certainly of value, the reader desiring a briefer and less detailed introduction to the subject might skip the remainder at Ž rst reading. This text is a revision of the book by Arnold, Costillo, and Sarabia (1992). The current version is of similar breadth, but with much more depth than the original. The text is clearly written and accessible with relatively few mathematical prerequisites. I found surprisingly few typographical errors; the authors are to be congratulated for this. In a few cases, regularity conditions for results are not given in full. Generally, this causes little confusion, although something does appear to be missing in the statement of Aczél’s key theorem (Theorem 1.3). Fortunately, most of the results in the sequel are derived from corollaries to this theorem, and the corollaries are stated more precisely. I noted few gaps in the material covered. The only area that I thought was insufŽ ciently represented was application to Markov chain Monte Carlo. Conditional speciŽ cation is particularly important in Gibbs sampling. I believe that many practitioners would beneŽ t from a discussion of the issues involved in these sampling schemes. Each chapter contains numerous exercises. These exercises appear to be at an appropriate level for a graduate course in statistics, and appear to provide appropriate reinforcement for the material in the preceding chapters.
Citations
More filters
Journal ArticleDOI
TL;DR: A method to measure the plausibility of each area being part of a possible localized anomaly in the map of rates and find intensity bounds for the delineation of spatial clusters in maps of areas with known populations and observed number of cases is proposed.
Abstract: Background There is considerable uncertainty in the disease rate estimation for aggregated area maps, especially for small population areas. As a consequence the delineation of local clustering is subject to substantial variation. Consider the most likely disease cluster produced by any given method, like SaTScan, for the detection and inference of spatial clusters in a map divided into areas; if this cluster is found to be statistically significant, what could be said of the external areas adjacent to the cluster? Do we have enough information to exclude them from a health program of prevention? Do all the areas inside the cluster have the same importance from a practitioner perspective?

201 citations

Journal ArticleDOI
TL;DR: In this paper, a multivariate exchangeable pairs approach was proposed to assess distributional distances to potentially singular multivariate normal distributions, which allows for a normal approximation even when the corresponding statistics of interest do not lend themselves easily to Stein's exchangeable pair approach.
Abstract: In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a higher-dimensional space, we also propose an embedding method which allows for a normal approximation even when the corresponding statistics of interest do not lend themselves easily to Stein's exchangeable pairs approach. To illustrate the method, we provide the examples of runs on the line as well as double-indexed permutation statistics.

145 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present the basic principles and recent advances in the area of statistical process control charting with the aid of runs rules, and briefly discuss the Markov chain approach which is the most popular technique for studying the run length distribution of run based control charts.
Abstract: The aim of this paper is to present the basic principles and recent advances in the area of statistical process control charting with the aid of runs rules. More specifically, we review the well known Shewhart type control charts supplemented with additional rules based on the theory of runs and scans. The motivation for this article stems from the fact that during the last decades, the performance improvement of the Shewhart charts by exploiting runs rules has attracted continuous research interest. Furthermore, we briefly discuss the Markov chain approach which is the most popular technique for studying the run length distribution of run based control charts.

136 citations

Journal ArticleDOI
TL;DR: Shewhart-type distribution-free control charts are considered for the known in-control median of a continuous process distribution based on the Wilcoxon signed-rank statistic and some runs type rules and can have better out-of-control performance than the Shewhart X-bar chart and the basicsigned-rank chart for the normal distribution and for some heavy-tailed distributions.
Abstract: Shewhart-type distribution-free control charts are considered for the known in-control median of a continuous process distribution based on the Wilcoxon signed-rank statistic and some runs type rules. The new charts are more attractive to the practitioner than a basic Shewhart-type signed-rank chart proposed by Bakir (2004), as they offer more desirable (smaller) false alarm rates and (larger) in-control average run-lengths, and can be easily implemented. In addition to being nonparametric, that is with a known and stable in-control performance for all continuous distributions, a simulation study indicates that the proposed charts can have better out-of-control performance than the Shewhart X-bar chart and the basic signed-rank chart for the normal distribution and for some heavy-tailed distributions such as the double exponential and the Cauchy. A numerical example is provided.

120 citations

Journal ArticleDOI
TL;DR: The computational aspects of calculating the hitting probability of spaced seeds are studied; and an efficient algorithm for identifying optimal spaced seeds is proposed.

79 citations

References
More filters
Journal ArticleDOI
TL;DR: A method to measure the plausibility of each area being part of a possible localized anomaly in the map of rates and find intensity bounds for the delineation of spatial clusters in maps of areas with known populations and observed number of cases is proposed.
Abstract: Background There is considerable uncertainty in the disease rate estimation for aggregated area maps, especially for small population areas. As a consequence the delineation of local clustering is subject to substantial variation. Consider the most likely disease cluster produced by any given method, like SaTScan, for the detection and inference of spatial clusters in a map divided into areas; if this cluster is found to be statistically significant, what could be said of the external areas adjacent to the cluster? Do we have enough information to exclude them from a health program of prevention? Do all the areas inside the cluster have the same importance from a practitioner perspective?

201 citations

Journal ArticleDOI
TL;DR: In this paper, a multivariate exchangeable pairs approach was proposed to assess distributional distances to potentially singular multivariate normal distributions, which allows for a normal approximation even when the corresponding statistics of interest do not lend themselves easily to Stein's exchangeable pair approach.
Abstract: In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a higher-dimensional space, we also propose an embedding method which allows for a normal approximation even when the corresponding statistics of interest do not lend themselves easily to Stein's exchangeable pairs approach. To illustrate the method, we provide the examples of runs on the line as well as double-indexed permutation statistics.

145 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present the basic principles and recent advances in the area of statistical process control charting with the aid of runs rules, and briefly discuss the Markov chain approach which is the most popular technique for studying the run length distribution of run based control charts.
Abstract: The aim of this paper is to present the basic principles and recent advances in the area of statistical process control charting with the aid of runs rules. More specifically, we review the well known Shewhart type control charts supplemented with additional rules based on the theory of runs and scans. The motivation for this article stems from the fact that during the last decades, the performance improvement of the Shewhart charts by exploiting runs rules has attracted continuous research interest. Furthermore, we briefly discuss the Markov chain approach which is the most popular technique for studying the run length distribution of run based control charts.

136 citations

Journal ArticleDOI
TL;DR: Shewhart-type distribution-free control charts are considered for the known in-control median of a continuous process distribution based on the Wilcoxon signed-rank statistic and some runs type rules and can have better out-of-control performance than the Shewhart X-bar chart and the basicsigned-rank chart for the normal distribution and for some heavy-tailed distributions.
Abstract: Shewhart-type distribution-free control charts are considered for the known in-control median of a continuous process distribution based on the Wilcoxon signed-rank statistic and some runs type rules. The new charts are more attractive to the practitioner than a basic Shewhart-type signed-rank chart proposed by Bakir (2004), as they offer more desirable (smaller) false alarm rates and (larger) in-control average run-lengths, and can be easily implemented. In addition to being nonparametric, that is with a known and stable in-control performance for all continuous distributions, a simulation study indicates that the proposed charts can have better out-of-control performance than the Shewhart X-bar chart and the basic signed-rank chart for the normal distribution and for some heavy-tailed distributions such as the double exponential and the Cauchy. A numerical example is provided.

120 citations

Journal ArticleDOI
TL;DR: The computational aspects of calculating the hitting probability of spaced seeds are studied; and an efficient algorithm for identifying optimal spaced seeds is proposed.

79 citations