  We establish in this paper \emph{a priori} global $W^{2,\delta}$ estimates
for singular fully nonlinear elliptic equations with $L^n$ right hand side
terms. The method is to slide paraboloids and barrier functions vertically to
touch the solution of the equation, and then to estimate the measure of the
contact set in terms of the measure of the vertex point set. To derive global
estimates from $L^n$ data, the Hardy-Littlewood maximal functions, appropriate
localizations and a new type of covering argument are adopted. These methods
also provide us a more direct proof of the $W^{2,\delta}$ estimates for
(nonsingular) fully nonlinear elliptic equations established by L. A.
Caffarelli and X. Cabr\'{e}.
