1,721,015 research outputs found
Depth-based classification of directional data
No full textA non-parametric procedure based on the concept angular depth function is developed for dealing with classification problems of objects in directional statistics. Several notions of depth for directional data are adopted: the angular simplicial, the angular Tukey’s, the arc distance, the cosine distance and the chord distance depths. The proposed method is flexible and can be applied even in high-dimensional cases when a suitable notion of depth is adopted. Performances are investigated and compared by applying methods to different distributional settings through simulated and real data sets
Non-parametric multivariate control charts based on data depth notion
No full textA control chart is used to monitor a process variable over time by providing information about the process behavior. Monitoring the process of related variables is usually called a multivariate quality control problem. Multivariate control charts, needed when dealing with more than one quality variable, relies on very specific models for the data generating process. When large historical data set are available, previous knowledge of the process may not be available or a unique model for all the features cannot be adopted, and no specific parametric model turns out to be appropriate and some alternative solutions should be adopted. Hence, exploiting non-parametric methods to build a control chart appears a reasonable choice. Non-parametric control charts require no distributional
assumptions on the process data and generally enjoy more robustness, i.e. are less sensitive to outlier, over parametric control schemes. Among the possible non-parametric statistical techniques, data depth functions are gaining a growing interest in multivariate quality control. These are nonparametric functions which are able to provide a dimension reduction to high-dimensional problems.
Several depth measures are effective for purposes, even in the case of deviation from the normality assumption. However, the use of the L^p data depth for constructing nonparametric multivariate control charts has been neglected so far. Hence, the contribution of this work is to discuss how a non-parametric approach based on the notion of the L^p data depth function can be exploited in the
Statistical Process Control framework
Adjusted Concordance Index: an Extensionl of the Adjusted Rand Index to Fuzzy Partitions
No full textIn comparing clustering partitions, the Rand index (RI) and the adjusted Rand index (ARI) are commonly used for measuring the agreement between partitions. Such external validation indexes can be used to quantify how close the clusters are to a reference partition (or to prior knowledge about the data) by counting classified pairs of elements. To evaluate the solution of a fuzzy clustering algorithm, several extensions of the Rand index and other similarity measures to fuzzy partitions have been proposed. An extension of the ARI for fuzzy partitions based on the normalized degree of concordance is proposed. The performance of the proposed index is evaluated through Monte Carlo simulation studies
Una prima datazione lichenometrica per la determinazione dell’epoca di riesposizione del paleostrato impresso
No full textRobust mean-variance portfolio through the weighted Lp depth function
No full textPortfolios constructed by the classical mean-variance model are very sensitive to outliers. We propose the use of a non-parametric estimation method based on statistical data depth functions. Specifically, we exploit the notion of the weighted Lp depth function to obtain robust estimates of the mean and covariance matrix of the asset returns. This approach has the advantage to be independent of parametric assumptions, and less sensitive to changes in the asset return distribution than traditional techniques. The proposed procedure is evaluated and compared with standard and other robust techniques through simulated and real data. Results indicate effective improvements of the proposed method in terms of out-of-sample performance
A boxplot for circular data
No full textThe box-and-whiskers plot is an extraordinary graphical tool that provides a quick visual summary of an observed distribution. In spite of its many extensions, a really suitable boxplot to display circular data is not yet available. Thanks to its simplicity and strong visual impact, such a tool would be especially useful in all fields where circular measures arise: biometrics, astronomy, environmetrics, Earth sciences, to cite just a few. For this reason, in line with Tukey's original idea, a Tukey-like circular boxplot is introduced. Several simulated and real datasets arising in biology are used to illustrate the proposed graphical tool
A note on depth-based classification of circular data
No full textA procedure is developed in order to deal with the classification problem of objects in circular statistics. It is fully nonparametric and based on depth functions for directional data. Using the so-called DD-plot, we apply the knearest neighbors method in order to discriminate between competing groups. Three different notions of data depth for directional data are considered: the
angular simplicial, the angular Tukey and the arc distance. We investigate and compare their performances through the average accuracy rate by means of simulated and real data sets
The zonoid region parameter depth
Full text linkSpanish Ministry of Science and Innovation [grants
PID2021-123592OB-I00 and TED2021-129316B-I00]; the Principality of Asturias/FEDER [grants GRUPIN-IDI2018-000132 and SV-PA-21-AYUD/2021/50897]; the Spanish Ministry of Science and Innovation [grants PID2019-104486GB-I00 and MTM2015-63971-P
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