Measuring the stability of histogram appearance when the anchor position is changed

Simonoff, Jeffrey S.; Udina, Frederic

doi:10.1016/s0167-9473(96)00040-0

Cited by 27 publications

(16 citation statements)

References 30 publications

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“…Their widespread use notwithstanding, the generation of a histogram is affected by well-known issues (see Silverman 1986;Simonoff & Udina 1997). Different bin widths and anchor positions can make histograms built from the same data look utterly dissimilar.…”

Section: Methodsmentioning

confidence: 99%

Astrophysical properties of star clusters in the Magellanic Clouds homogeneously estimated by ASteCA

Perren

Piatti

Vazquez

2017

A&A

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Aims. We seek to produce a homogeneous catalog of astrophysical parameters of 239 resolved star clusters, located in the Small and Large Magellanic Clouds, observed in the Washington photometric system. Methods. The cluster sample was processed with the recently introduced Automated Stellar Cluster Analysis (ASteCA) package, which ensures both an automatized and a fully reproducible treatment, together with a statistically based analysis of their fundamental parameters and associated uncertainties. The fundamental parameters determined for each cluster with this tool, via a color-magnitude diagram (CMD) analysis, are metallicity, age, reddening, distance modulus, and total mass. Results. We generated a homogeneous catalog of structural and fundamental parameters for the studied cluster sample and performed a detailed internal error analysis along with a thorough comparison with values taken from 26 published articles. We studied the distribution of cluster fundamental parameters in both Clouds and obtained their age-metallicity relationships. Conclusions. The ASteCA package can be applied to an unsupervised determination of fundamental cluster parameters, which is a task of increasing relevance as more data becomes available through upcoming surveys.

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Section: Methodsmentioning

confidence: 99%

Astrophysical properties of star clusters in the Magellanic Clouds homogeneously estimated by ASteCA

Perren

Piatti

Vazquez

2017

A&A

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“…The so called "anchor position" of the histogram (see [36]) is thus chosen here as x (1) . Regular histogram procedures reduce to rules for determining an optimal number m opt of bins that minimizes some type of risk in selecting a histogram from (2.5):…”

Section: Histogram Proceduresmentioning

confidence: 99%

A comparison of automatic histogram constructions

et al. 2009

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Abstract. Even for a well-trained statistician the construction of a histogram for a given real-valued data set is a difficult problem. It is even more difficult to construct a fully automatic procedure which specifies the number and widths of the bins in a satisfactory manner for a wide range of data sets. In this paper we compare several histogram construction procedures by means of a simulation study. The study includes plug-in methods, cross-validation, penalized maximum likelihood and the taut string procedure. Their performance on different test beds is measured by their ability to identify the peaks of an underlying density as well as by Hellinger distance.Mathematics Subject Classification. 62G05, 62G07.

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“…Hence, in order to minimize the MISE H−BK , we obtain the histogram-kernel error asymptotic optimal bin width (16) and the asymptotic MISE H−BK :…”

Section: Theorem 21mentioning

confidence: 99%

“…Simonoff & Udina [16] measured the stability of histogram appearance when the bin edge location is changed. In this paper, the author proposes a practical and efficient algorithm based on the Genetic Algorithm (GA) to determine the bin edge and bin width simultaneously for constructing the global optimal data-based histograms.…”

Section: Introductionmentioning

confidence: 99%

Histogram-kernel error and its application for bin width selection in histograms

Wang

Zhang

2009

Acta Math. Appl. Sin. Engl. Ser.

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Histogram and kernel estimators are usually regarded as the two main classical data-based nonparametric tools to estimate the underlying density functions for some given data sets. In this paper we will integrate them and define a histogram-kernel error based on the integrated square error between histogram and binned kernel density estimator, and then exploit its asymptotic properties. Just as indicated in this paper, the histogram-kernel error only depends on the choice of bin width and the data for the given prior kernel densities. The asymptotic optimal bin width is derived by minimizing the mean histogram-kernel error. By comparing with Scott's optimal bin width formula for a histogram, a new method is proposed to construct the data-based histogram without knowledge of the underlying density function. Monte Carlo study is used to verify the usefulness of our method for different kinds of density functions and sample sizes.

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Measuring the stability of histogram appearance when the anchor position is changed

Cited by 27 publications

References 30 publications

Astrophysical properties of star clusters in the Magellanic Clouds homogeneously estimated by ASteCA

Astrophysical properties of star clusters in the Magellanic Clouds homogeneously estimated by ASteCA

A comparison of automatic histogram constructions

Histogram-kernel error and its application for bin width selection in histograms

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