  This paper develops detailed mathematical statistical theory of a new class
of cross-validation techniques of local linear kernel hazards and their
multiplicative bias corrections. The new class of cross-validation combines
principles of local information and recent advances in indirect
cross-validation. A few applications of cross-validating multiplicative kernel
hazard estimation do exist in the literature. However, detailed mathematical
statistical theory and small sample performance are introduced via this paper
and further upgraded to our new class of best one-sided cross-validation. Best
one-sided cross-validation turns out to have excellent performance in its
practical illustrations, in its small sample performance and in its
mathematical statistical theoretical performance.
