Question: Nonlinear Regression Consider the nonlinear regression model y 2 t = 0 + 1xt + ut , ut iid N(0, 1). (a) Write down

Nonlinear Regression Consider the nonlinear regression model y β2 t = β0 + β1xt + ut , ut ∼ iid N(0, 1).

(a) Write down the distributions of ut and yt .

(b) Show how you would estimate this model’s parameters by maximum likelihood using: (i) the Newton-Raphson algorithm; and (ii) the BHHH algorithm.

(c) Briefly discuss why the Gauss-Newton algorithm is not appropriate in this case.

(d) Construct a test of the null hypothesis β2 = 1, using: (i) a LR test; (ii) a Wald test; (iii) a LM test with the information matrix based on the outer product of gradients; and (iv) a LM test based on two linear regressions.

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