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Yl= f (X,, 80)+ Et(t= 1, 2,..., n) where f:~'xe-+ I is a known function measurable on~'for each 8 in e, and continuous on e, a compact subset of~ P; 80 is an unknown vector contained in e; and (Xt'Et) is a sequence of independent not identically distributed random vectors. yt and Xt are observable, but Et is not.

The problem is to obtain an estimate of the unknown parameter (Jo given observations (y,. X,) and a kn () wlpr! g~ of f A na. tura. l approach to thi3 problcm i~ to consider the nonlinear weighted least squares estimator On which solves the problem