title: ÐÑÑÐ²Ð»ÐµÐ½Ð¸Ðµ Ð²ÑÐ±ÑÐ¾ÑÐ¾Ð² Ð¸ Ð°Ð½Ð¾Ð¼Ð°Ð»Ð¸Ð¹ ÑÐ¸Ð¿Ð° ÑÐ´Ð²Ð¸Ð³ Ð² Ð´Ð°Ð½Ð½ÑÑ Ð»Ð°Ð·ÐµÑÐ½Ð¾Ð¹ Ð»Ð¾ÐºÐ°ÑÐ¸Ð¸ ÐÑÐ½Ñ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð½ÐµÑÐ°Ð²ÐµÐ½ÑÑÐ²Ð° Ð§ÐµÐ±ÑÑÐµÐ²Ð°
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Outlier and shift detection based on the Chebyshev inequality in LLR data
Creators: name: ÐÐ°Ð½, ÐÐ°ÑÐ³Ð°ÑÐ¸ÑÐ°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: Ð»Ð°Ð·ÐµÑÐ½Ð°Ñ Ð»Ð¾ÐºÐ°ÑÐ¸Ñ ÐÑÐ½Ñ
Ð°Ð½Ð¾Ð¼Ð°Ð»Ð¸Ñ
Ð²ÑÐ±ÑÐ¾Ñ
ÑÐ´Ð²Ð¸Ð³
ÑÑÐµÐ´Ð½ÐµÐµ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ðµ
ÑÑÐ°Ð½Ð´Ð°ÑÑÐ½Ð°Ñ Ð¾ÑÐ¸Ð±ÐºÐ° ÑÑÐµÐ´Ð½ÐµÐ³Ð¾
Ð½ÐµÑÐ°Ð²ÐµÐ½ÑÑÐ²Ð° ÑÐ¸Ð¿Ð° ÐÐ°ÑÑÑÐ°-Ð§ÐµÐ±ÑÑÐµÐ²Ð°
Ð½ÐµÑÐ°Ð²ÐµÐ½ÑÑÐ²Ð¾ Ð§ÐµÐ±ÑÑÐµÐ²Ð°
Ð´Ð¾Ð²ÐµÑÐ¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»
Ð¼Ð¸Ð½Ð¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ Ð²ÐµÑÑ Ð½ÐµÐ¹ Ð³ÑÐ°Ð½Ð¸ÑÑ Ð±Ð°Ð¹ÐµÑÐ¾Ð²ÑÐºÐ¾Ð³Ð¾ ÑÐ¸ÑÐºÐ°
Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ ÑÐµÑÑÐ¾Ð²ÑÑ Ð´Ð°Ð½Ð½ÑÑ
Lunar laser ranging
anomaly
outlier
shift
mean-value
standard error
Gauss-Chebyshev type inequalities
Chebyshev inequality
confidence interval
minimizing the upper bound of Bayesian risk
test data modelling

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description: The given work is devoted to developing the outlier and shift detection algorithm and applying it to LLR data. The observations are presented as pairs of mean and their standard deviations. These pairs are not real observations but summaries on their groups. An outlier in the data of this type is an observation which significantly differs from the neighbouring ones, while a shift is a significant change of means and/or standard errors over time. As far as we know, for today there is no universal algorithm which allows detecting anomalies in data of this type. However, this task could be solved using the Gauss-Chebyshev type inequalities. These inequalities let us determine so-called confidence intervals considering which allows us to move on the other problem of minimizing the upper bound of Bayesian risk under the natural constraints. Since performance evaluation on the real data does not seem possible, the analysis of real data in order to model similar test data was carried out. The algorithm showed good results for test data. We also obtained satisfactory results for real data. The work was fulfilled on the premises of IAA RAS, where we were provided real LLR data considered in the given paper. The algorithm is supposed to be implemented in the software system of data preprocessing of IAA RAS.