Weak consistency and asymptotic normality of the ordinary least squares estimator in a linear regression with adaptive learning is derived when crucial, so-called, ‘gain’ parameter estimated first step by nonlinear from an auxiliary model.

Rota and Laitila (2015) suggest an alternative two-step calibration estimation resulting from combining two approaches, i.e., linear (Särndal Lundström, 2005) propensity score (Chang Kott, 2008), when the functional form of response probability is assumed to be known. The first step focuses on estimating this function second total a survey variable. This paper extends these previous findings by...

‎In this article‎, ‎we develop two nonparametric smoothing estimators for parameter of a time-variant parametric model‎. ‎This parameter can be from any parametric family or from any parametric or semi-parametric regression model‎. ‎Estimation is based on a two-step procedure‎, ‎in which we first get the raw estimate of the parameter at a set of disjoint time...