We study the parameter estimation in a nonlinear regression model with a general error's structure,strong consistency and strong consistency rate of the least squares estimator are obtained.
In this paper we study the Cauchy problem for a class of semi-linear parabolic type equations with weak data in the homogeneous spaces. We give a method which can be used to construct local mild solutions of the abstract Cauchy problem in? σ,s,p andL q([0, T);H s,p) by introducing the concept of both admissible quintuplet and compatible space and establishing time-space estimates for solutions to the linear parabolic type equations. For the small data, we prove that these results can be extended globally in time. We also study the regularity of the solution to the abstract Cauchy problem for nonlinear parabolic type equations in ?σ,s,p. As an application, we obtain the same result for Navier-Stokes equations with weak initial data in homogeneous Sobolev spaces.
