Convergence in distribution of a normalized projective estimate for an infinite-dimensional parameter of linear regression. (English. Ukrainian original) Zbl 0840.62062

Kukush, A. G.

Theory Probab. Math. Stat. 48, 69-75 (1994); translation from Teor. Jmovirn. Mat. Stat. 48, 101-110 (1993).

Summary: A projective estimate for a parameter belonging to a closed set \(\Theta\) is constructed in the model of linear regression in a Hilbert space \(H\) with non-correlated noise. To obtain the estimate, the weighted method of least squares is used. The coordinates of the parameter are treated in groups, each group being observed independently of the others. The conditions for convergence in distribution of finite-dimensional projections of the normalized estimate are obtained. When \(\Theta\) is an ellipsoid, the conditions for convergence in distribution of the normalized estimate in \(H\) are presented.

MSC:

62J05	Linear regression; mixed models
62J99	Linear inference, regression
62H99	Multivariate analysis
60B12	Limit theorems for vector-valued random variables (infinite-dimensional case)

Keywords:

non-correlated noise; projective estimate; Hilbert space; weighted method of least squares; convergence in distribution of finite-dimensional projections