Abstract:An adaptive estimator (of a slope parameter) based on rank statistics is constructed and its asymptotic optimality is studied. A complete orthonormal system is incorporated in the adaptive determination of the score generating function. The proposed sequential procedure is based on a suitable stopping rule. Various properties of the sequential adaptive procedure and the stopping rule are studied. Asymptotic linearity results of linear rank statistics are also studied and some rates of the convergence are established.
Keywords: asymptotically optimal score generating function, Fisher information, orthonormal system, rank $(R-)$-estimator, stopping rule, asymptotically optimal estimators
AMS Subject Classification: 62G05, 62G20