Journal of the
Korean Mathematical Society JKMS

In [5], Cs$\ddot{\rm o}$rg\H{o} and Zitikis exposed the strong uniform-over-$[0,~\infty)$ consistency, and weak uniform-over-$[0, ~\infty)$ approximation of the empirical mean residual life process by employing weight functions. We carry on the uniform asymptotic behaviors of the empirical mean residual life process over the whole positive half line by representing the process as an integral form. We compare our results with those of Yang [15], Hall and Wellner [8], and Cs$\ddot{\rm o}$rg\H{o} and Zitikis [5].

Keywords: empirical mean residual life process, uniform law of large numbers, uniform central limit theorem, uniform law of the iterated logarithm

MSC numbers: Primary 62N05, 62G15; Secondary 60F17, 60F99