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CLT for statistics employed in selection of the most significant factorsтезисы доклада
- Автор: Bulinski A.V.
- Сборник: Abstracts of Communications of Russian-Chinese Seminar on Asymptotic Methods in Probability Theory and Mathematical Statistics, St. Petersburg, June 10-14, 2013
- Тезисы
- Год издания: 2013
- Место издания: St. Petersburg
- Первая страница: 20
- Последняя страница: 21
- Аннотация: The problem of identi cation of the most signi cant factors which determine the behavior of a response variable is not only of theoretical interest, being motivated by applications. Actually, such problem arises, e.g., in medical and biological studies. There the response variable can characterize the health state of a patient and factors represent the genetic (a collection of single-nucleotide polymorphisms) and non-genetic (or environmental) data. A widely used approach to the mentioned problem is based on the multifactor dimensionality reduction (MDR) method introduced by M.Rithchie et al.(2001). This method was developed in a number of papers. Recently the basis for employment of the MDR method with arbitrary penalty function was provided by A.Bulinski (2012). Namely, the necessary and sufficient conditions were found to guarantee the strong consistency of statistics used to analyze the relevant prediction error for response variable. Moreover, the choice of the penalty function proposed by D.R.Velez et al. (2007) is clari ed. In this talk we consider the regularization of statistics introduced by A.Bulinski (2013) which permits to prove for them the central limit theorem. The main difficulty here is due to the cross-validation procedure. We also discuss the importance measures for various collections of factors.
- Добавил в систему: Булинский Александр Вадимович