The Gap statistic is a standard method for determining the number of clusters in a set of data. The Gap statistic standardizes the graph of log(Wk), where Wk is the within-cluster dispersion, by comparing it to its expectation under an appropriate null reference distribution of the data. We suggest to use Wk instead of log(Wk), and to compare it to the expectation of Wk under a null reference d...

The Gender-Age-Physiology (GAP) model is a validated, baseline-risk prediction model for mortality in idiopathic pulmonary fibrosis. Longitudinal variables have been shown to contribute to risk prediction in idiopathic pulmonary fibrosis and may improve the predictive performance of the baseline GAP model. Our aims were to further validate the GAP model and evaluate whether the addition of long...

A key contribution of this paper is a county-level dataset to study how differences in school quality across locations and races in the South ultimately affected labor market outcomes. Prior to the construction of this data, investigation of this question would have been limited to the use of state-level averages of school quality metrics. These state-level averages are suboptimal for two reaso...

SenseClusters is a freely available system that clusters similar contexts. It can be applied to a wide range of problems, although here we focus on word sense and name discrimination. It supports several different measures for automatically determining the number of clusters in which a collection of contexts should be grouped. These can be used to discover the number of senses in which a word i...

The presence of multiple luminous galaxies in clusters can be explained by the finite time over which a galaxy sinks to the center of the cluster and merges with the the central galaxy. The simplest measurable statistic to quantify the dynamical age of a system of galaxies is the luminosity (magnitude) gap, which is the difference in photometric magnitude between the two most luminous galaxies....

In this paper, we perform one of the first empirical tests comparing several existing algorithms for determining the number of clusters in a data set (the gap statistic, X-means, G-means, data spectroscopic clustering and self-tuning spectral clustering). We use a large number of data sets randomly generated with varying distributions and parameters. The results show that the G-means and X-mean...

A wide literature is available on the asymptotic behavior of the Durbin-Watson statistic for autoregressive models. However, it is impossible to find results on the Durbin-Watson statistic for autoregressive models with adaptive control. Our purpose is to fill the gap by establishing the asymptotic behavior of the Durbin Watson statistic for ARX models in adaptive tracking. On the one hand, we ...

Many risk, inequality, poverty and concentration measures are extremely sensitive to outliers, dependence, heterogeneity and heavy tails. In this paper we focus on robust measurement of risk, inequality, poverty and concentration under heterogeneity, dependence and heavy-tailedness of largely unknown form using the recent results on t−statistic based heterogeneity and correlation robust inferen...