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

with ξ1, . . . , ξN a sequence of independent identically distributed random variables satisfying the conditions Eξi = 0, Dξi = 1. (1.2) Moreover, the values ai > 0 and bi > 0 are assumed known, while the values of the parameter θ and the variances DXi ≡ σ i are unknown. The values of the random variables ξ1, . . . , ξN are assumed unknown either. In this article, we study the problem of estimating the unknown parameter θ > 0 from the observations X1, . . . , XN . This problem is a particular instance of the nonlinear regression problem which is usually solved by the method of least squares or its modifications. Searching an estimator approximately, we often use linearization methods, the steepest descent method, etc. (see, for instance, [1]) whose implementation requires application of computers in view of a huge number of iterations. However, it turns out that for a linear-fractional regression problem of the form (1.1) the simple estimator