Asymptotically Normal Estimation of a Multidimensional Parameter in the Linear-fractional Regression Problem

are known numbers. The random variables ξi, i = 1, . . . , N , in (1.1) are nonobservable measurement errors. Below we impose some constraints on the limit behavior of the distributions of some linear combinations of these random variables. In this article we consider the problem of estimating the unknown vector θ with coordinates θj > 0, j = 1, . . . ,m, through the random variables Z1, . . . , ZN . We propose some rather simple method for obtaining asymptotically normal estimators of unknown parameters for the linear-fractional regression model (1.1)–(1.3). Unlike the method of least squares which is usually used for solving such nonlinear regression problems, implementation of the proposed method does not require iterational procedures which in turn create difficulties in selecting initial approximation, convergence rate of the process, etc. and necessitate employment of computers due to a huge number of iterations. The main goal of this article is to describe the method for constructing estimators in its general form together with the scheme of studying these estimators, as well as to demonstrate application of some ideas that can be used in studying the estimators. A mathematically-rigorous complete justification of the method was given in [1] in the simplest one-dimensional case of the linear-fractional regression problem. In a forthcoming article, the authors thoroughly study the case