A Method of Searching for Extreme Observations in a Problem of Fuzzy Regression

  • И.В. Пономарев Алтайский государственный университет (Барнаул, Россия)
  • Т.В. Саженкова Алтайский государственный университет (Барнаул, Россия)
  • В.В. Славский Югорский государственный университет (Ханты-Мансийск, Россия)
Keywords: fuzzy regression, statistical outliers, Legendre transformation, convex analysis


The study of statistical data for outliers is an urgent task of modern mathematics. The reliability of these methods directly affects the quality of the subsequent processing of statistical data sets and the adequacy of the resulting conclusions. In general, all available observations should be checked and compared with a certain numerical indicator. The further conclusion should be made by comparing these indicators among themselves.

In this paper, a technique to search for statistical outliers for one of the possible regression models based on the Chebyshev norm is considered. The proposed approach is based on the Legendre transformation, one of the known transformations used in the convex analysis. This algorithm allows us to refer to the group of statistical outliers for a set of observations and not for individual observations. This key point distinguishes this algorithm from the most of the commonly used algorithms. This way, the task can be solved in one pass with less required time. An example of the study of a sample for outliers is presented. The possibility to compare the obtained characteristics provides the opportunity to solve the problem for a different number of assumed extreme values.

DOI 10.14258/izvasu(2018)4-18


Download data is not yet available.


Tanaka H., Hayashi I., Watada J. Possibilistic Linear Regression Analysis with Fuzzy Model // European Journal of Operational Research. — 1989. — V. 40.

Дрейпер Н, Смит Г. Прикладной регрессионный анализ. Множественная регрессия = Applied Regression Analysis. — 3-е изд. — М., 2007.

Gomez A.T., Sanchez, Jorge de Andres. Applications Of Fuzzy Regression In Actuarial Analysis // Journal of Risk & Insurance. — 2003. — V. 30.

Стрижов В.В., Крымова Е.А. Методы выбора регрессионных моделей. — М., 2010.

Cook R.D. Detection of Influential Observation in Linear Regression // Technometrics. — 1977. — Vol. 19, № 1.

Andrews D.F., Pregibon D. Finding the outliers that matter // Journal of the Royal Statistical Society. — 1978. — Vol. 40.

Weisberg S. Applied linear regression, 3rd ed. — Jonh Wiley & Sans, Inc., 2005.

Пономарев И.В., Славский В.В. Нечеткая модель линейной регрессии // Доклады Академии наук. — 2009. — Т. 428, № 5.

Ponomarev I.V., Slavsky V.V. Uniformly fuzzy model of linear regression // Journal of Mathematical Sciences. — 2012. — Vol. 186, issue 3.

Куркина М.В., Пономарев И.В. Система нечетких отношений равенств в банаховом пространстве // Дифференциальные уравнения. Функциональные пространства. Теория приближений. Международная конференция, посвященная 100-летию со дня рождения С. Л. Соболева (Новосибирск, 5-12 октября 2008 г.) : тезисы докладов. — Новосибирск, 2008.
How to Cite
Пономарев, И., Саженкова, Т., & Славский, В. (2018). A Method of Searching for Extreme Observations in a Problem of Fuzzy Regression. Izvestiya of Altai State University, (4(102), 98-101. https://doi.org/https://doi.org/10.14258/izvasu(2018)4-18
Математика и механика