The structure of polynomials of asymptotic expansions of the least square estimate and variance estimate. (English. Ukrainian original) Zbl 0937.62065

Bardadym, T. O.

Theory Probab. Math. Stat. 53, 1-6 (1996); translation from Teor. Jmovirn. Mat. Stat. 53, 1-5 (1995).

A nonlinear regression model with i.i.d. random errors is investigated. In the paper of A.V. Ivanov and the author, Theory Probab. Math. Stat. 33, 11-20 (1986); translation from Teor. Veroyatn. Mat. Stat. 33, 11-20 (1985; Zbl 0632.62089), the asymptotic expansions of the least-squares estimates as well as expansions of estimates of variance are obtained. These expansions are homogeneous polynomials of random arguments that depend on the regression parameters.
In this paper the structure of the polynomial coefficients that depend on the derivatives of the regression function is investigated. These polynomial coefficients are useful for obtaining the asymptotic expansions of jack-knife estimates as well as cross-validation estimates of the regression parameters.

Reviewer: O.G.Kukush (Kyïv)

MSC:

62J02	General nonlinear regression
62J99	Linear inference, regression

Keywords:

least-squares estimates; polynomial asymptotic expansions

Citations:

Zbl 0632.62089