Sequential procedures based on M-estimators with discontinuous score functions

Bounded-width sequential confidence intervals and sequential tests for regression parameter based on M-estimators are extended to the case where the score-functions generating the M-estimators have jump-discontinuities. In the context of the asymptotic normality of the stopping variable, for the confidence interval problem, it is observed that the jump-discontinuities induce a slower rate of convergence. The proofs of the main theorems rest on the weak convergence of some related processes and this is also studied.