ABSTRACT
A crucial assumption for the methods developed in Chapters 3 through 6 is the linear conditional mean assumption (LCM( β $ \beta $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math7_1.tif"/> )) and the constant conditional variance assumption (CCV( β $ \beta $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math7_2.tif"/> )). In this chapter we study the theoretical relation between the linear conditional mean condition and elliptical distribution, and introduce a method to transform a set of vectors into roughly multivariate normal random vectors to satisfy the LCM( β $ \beta $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math7_3.tif"/> ) and CCV( β $ \beta $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math7_4.tif"/> ).
