B0534
Title: On the minimum variance squared regression
Authors: Zinoviy Landsman - University of Haifa (Israel) [presenting]
Udi Makov - University of Haifa (Israel)
Abstract: Uncertainty is a common feature in many different types of statistical, actuarial and economic models. It is important to quantify and measure uncertainty to make informed decisions and manage risk effectively. Various measures of uncertainty exist, including standard deviation, variance, and confidence intervals. In a search for a measure of uncertainty, a recent study introduced a new functional, location of a minimum variance squared distance (LVS). The aim is to extend the use of the LVS to capture the uncertainty in regression models which are typically used to analyze the relationship between a dependent variable and one or more independent variables This function represents a vector of predictors in the minimum variance squared (MVS) sense. It is shown that under symmetric underlying distributions P of predicted vector Y, this functional is close to the traditional minimum expected squared (MES) functional. For non-symmetric underlying distributions of Y, MES and MVS are essentially different from each other and the difference is determined by the matrix of joint third moments of distribution P and the covariance matrix of vector Y. The analytical closed form for MVS functional is obtained and the mixture of both is considered: MVS and MES functionals. The numerical illustration of the prediction of returns of 6 international stock indexes by the returns of their dominant components is provided
