homokurtosis

— In terms of the original error u#95;i, this assumption implies that #92;mathrm#123;E#125;(u#95;i⁴#92;mid#92;mathbf#123;x#125;#95;i)#61;#92;mathit#123;constant#125;#92;equiv#92;kappa² under H#95;0. This is called the homokurtosis (constant conditional fourth moment) assumption. Homokurtosis always holds when u is independent of #92;mathbf#123;x#125;, but there are conditional distributions for which #92;mathrm#123;E#125;(u#92;mid#92;mathbf#123;x#125;)#61;0 and #92;mathrm#123;Var#125;(u#92;mid#92;mathbf#123;x#125;)#61;#92;sigma² but #92;mathrm#123;E#125;(u⁴#92;mid#92;mathbf#123;x#125;)#61;0 depends on #92;mathbf#123;x#125;.