
СЕМИНАРЫ 

Semiparametric alternation: convergence and efficiency В. Г. Спокойный^{} ^{} Институт прикладного анализа и стохастики им. Вейерштрасса 

Аннотация: A general problem of semiparametric estimation is considered when the target parameter The alternating approach assumes that the partial estimation of This naturally leads to the procedure based on sequential optimization: one starts from some initial value of Unfortunately, precise theoretical results addressing the overall quality of such procedures are only available in special cases. One example is given by linear models. In this case, an alternating procedure converges and is efficient under quite simple and tractable identifiability conditions. We propose a novel approach to systematic study of the quality and efficiency of such iterative procedures which can be viewed as a nonasymptotic analog of the Le Cam LAN theory. It allows for extending the algorithmic properties of the procedure like geometric convergence and efficiency from the linear to a general regular case. 