On the consistency of a spatial-type interval-valued median for random intervals

The sample $d_\theta$-median is a robust estimator of the central tendency or location of an interval-valued random variable. While the interval-valued sample mean can be highly influenced by outliers, this spatial-type interval-valued median remains much more reliable. In this paper, we show that under general conditions the sample $d_\theta$-median is a strongly consistent estimator of the $d_\theta$-median of an interval-valued random variable.Comment: 14 page

Bayesian Approach to News Recommendation Systems

This research was responsible for the development of a method for recommending news in online newspapers. This study takes into consideration that each reader has specific needs and interests when reading online newspapers, and it is a challenge to bring personalized and individualized information, in order to meet each reader's needs. The main goal here was solving or minimizing this problem when there is a new reader, because the system has little or no information over the reader’s preferences. This descriptive research used as a subject a new reader from a news portal and all data collected from the web browsing experience was performed without that user’s knowledge. The research may be characterized as applied, since it generated knowledge enough for solving the problem of online newspaper readers. A quantitative approach was adopted, because the news recommended by the system were classified and the system’s accuracy was quantified comparing the system`s suggestions and the decisions made by the readers. The solution adopted involved accessing three different methods. The Bayesian network was adopted as the main method when generating news suggestions to the new reader and the excess of variables was clustered using the K-means algorithm. The probabilities missing on this network were captured through the EM algorithm (Expectation Maximization). This algorithm uses cases in which variables were used to learn how to predict their values when they are not being observed

A spatial-type interval-valued median for random intervals

© 2018 Informa UK Limited, trading as Taylor & Francis Group. To estimate the central tendency or location of a sample of interval-valued data, a standard statistic is the interval-valued sample mean. Its strong sensitivity to outliers or data changes motivates the search for more robust alternatives. In this respect, a more robust location statistic is studied in this paper. This measure is inspired by the concept of spatial median and makes use of the versatile generalized Bertoluzza's metric between intervals, the so-called dθ distance. The problem of minimizing the mean dθ distance to the values the random interval takes, which defines the spatial-type dθ-median, is analysed. Existence and uniqueness of the sample version are shown. Furthermore, the robustness of this proposal is investigated by deriving its finite sample breakdown point. Finally, a real-life example from the Economics field illustrates the robustness of the sample dθ-median, and simulation studies show some comparisons with respect to the mean and several recently introduced robust location measures for interval-valued data.status: publishe