Notes on line dependent coefficient and multiaverage - Wilkowski, Andrzej (Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu, 2011)
In this paper we discuss new statistic tools which enable more precise economics data analysis. Firstly, we define line dependent coefficientas a cosine of the angle made of the cross of regression lines. This is the basis thanks to which we can define other nonlinear relation coefficients such as conic dependent coefficient. Just like the classic correlation coefficient, line dependent coefficient is also asymptotically normal. The second part of this article is about multiaverage, a generalization of the classic expected value of the random variable idea. The average may be considered as the root-mean-square average approximation of the random variable with one point. Multiaverage is an approximation of the random variable with more than just one point at the same time (which is important when we talk about random variables, whose distributions are mixtures, or about multimodal densities). While defining multiaverage, we use the standard moments method and some facts from the orthogonal polynomial theory. In this paper we give some numerical examples in which we use the aforementioned tools.
Mathematical Economics, 2011, Nr 7 (14), s. 241-251
Keywords: correlation