N. Lazrieva, T. Toronjadze

General M-Estimators in the Presence of Nuisance Parameters. Skew Projection Technique

A multidimensional parametric filtered statistical model is considered, the notions of the regularity and ergodicity of the model, as well as the notion of a general $M$-estimator are studied. A skew projection technique is proposed, by which we construct an $M$-estimator of the parameter of interest in the presence of nuisance parameters, which is asymptotically normal with the zero mean and the same covariance matrix as the corresponding block of the asymptotic covariance matrix of the full parameter's $M$-estimator.