Statistics & Probability Letters 18 (1993) 13-17 North-Holland 30 August 1993 Asymptotic theory of least squares estimator of a particular nonlinear regression model Debasis Kundu Department of Mathematics, Indian Institute of Technology tinpur, India Received January 1992 Revised February 1993 Abstract: The consistency and asymptotic normality of the least squares estimator are derived for a particular non-linear regression model, which does not satisfy the standard sufficient conditions of Jennrich (1969) or Wu (19811, under the assumption of normal errors. Keywords: Consistency; least squares estimator; non-linear regression. 1. Introduction The least squares method plays an important role in drawing inferences about the parameters in the non-linear regression model. Jennrich (1969) first rigorously proved the existence of the least squares estimator and showed its consistency of the following non-linear model: yt =f,(fI,) +EI, t = 1, 2 ).... (1.1) Jennrich proved the strong consistency of the least squares estimator i,, under the following assumption: zyxwvuts F,<tl,, 0,) converges uniformly to a continuous function F(B,, 0,) for all 8, and 8, and F(f?,, 0,) = 0 if and only if 8, = O,, where F,(%7 %) = $ ?r (f,(4) -f,(Q)‘. (1.2) Under some stronger assumptions, asymptotic normality was proved in the same paper. Wu (1981) gave some sufficient conditions under which the least squares estimator converges to BOalmost surely, when the growth rate requirement of F, is replaced by a Lipschitz type condition on the sequence fi. We consider the non-linear regression model yr = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA c0s(2deo) + E,, t = 1, 2,. . . , (l-3) where (~~1 are i.i.d. normal random variables with mean zero and finite positive variance u2. 8, is an Correspondence to: Debasis Kundu, Department of Mathematics, Indian Institute of Technology Kanpur, 11T Post Office, Kanpur 208016, India. 0167-7152/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved 13