Consider the nonlinear regression model (y=exp left(mathbf{x}^{prime} boldsymbol{beta} ight) /left[1+exp left(mathbf{x}^{prime} boldsymbol{beta} ight) ight]+u), where the error term is possibly heteroskedastic. (a) Within what range

Consider the nonlinear regression model \(y=\exp \left(\mathbf{x}^{\prime} \boldsymbol{\beta}\right) /\left[1+\exp \left(\mathbf{x}^{\prime} \boldsymbol{\beta}\right)\right]+u\), where the error term is possibly heteroskedastic.

(a) Within what range does this restrict \(\mathrm{E}[y \mid \mathbf{x}]\) to lie?

(b) Give the first-order conditions for the NLS estimator.

(c) Obtain the asymptotic distribution of the NLS estimator using result (5.77).

BNLS N[3,(D'D) 'D',D(D'D)'], (5.77)