- If we use Non-linear Least Squares to estimate a model that is a non-linear function of the parameters, then:
- The estimator will generally be consistent and asymptotically unbiased, but typically it will be biased in finite samples.
- The estimator will generally be consistent and Best Linear Unbiased.
- The estimator will generally be consistent and unbiased, but it is likely to be inefficient in finite samples.
- The estimator will generally be consistent and have an asymptotic sampling distribution that is normal, and it will be unbiased if the errors are normally distributed.

- When applying the Non-Linear Least Squares estimator, we need to find the "global" minimum of the objective function, rather than a "local" minimum, becuase:
- Otherwise the estimator will not usually be Best Linear Unbiased.
- Otherwise the estimator will not usually be consistent.
- Otherwise the estimator will not usually have a normal sampling distribution.
- Otherwise the estimator will not usually be efficient in finite samples.

- The Newton-Raphson algorithm for obtaining the Non-Linear Least Squares estimator has the following property:
- It works effectively if there are just a few parameters in the model, but not if there are many parameters.
- It may give different results if different starting values are chosen for the algorithm.
- It works extremely effectively if the objective function is close to being a quadratic function of the parameters.
- Both B and C.

- When we are using Non-Linear Least squares estimation, the usual "t-statistics" will be:
- Chi-square distributed in large samples, but not necessarily t-distributed in finite samples.
- Standard normally distributed in large samples.
- Standard normally distributed in large samples, but not necessarily t-distributed in finite samples.
- Student-t distributed in finite samples, and standard normally distributed if the sample size is very large.

- Check the EViews regression output located here. The following is true:
- Non-Linear Least Squares estimation has been used, and a global minimum of the objective function appears to have been found.
- Non-Linear Least Squares estimation has been used, and a local minimum of the objective function appears to have been found.
- Non-Linear Least Squares estimation has been used, but the algorithm has not really converged to a true minimum of the objective function.
- None of the above.

- If we estimate a non-linear regression model using the Non-Linear Least Squares (NLLS) estimator, and we wrongly omit one or more ariables from the model, then:
- The NLLS estimator will be biased, but consistent.
- The NLLS estimator will be both biased and inconsistent.
- The NLLS estimator will be unbiased, but inconsistent.
- The NLLS estimator will be unbiased and inconsistent, as long as the error-term has a zero mean.

- If we have a non-linear regression model with additive and normally distributed errors, then:
- The NLLS estimator of the coefficient vector will be asymptotically normally distributed.
- The usual t-statistics will be asymptotically normally distributed.
- All of A, B and D are correct.
- The NLLS estimator of the coefficient vector is the same as the Maximum Likelihood estimator for this vector.

- Check the EViews regression output located here. The following is true:
- The usual F-statistic does not appear in the output because there is no intercept in the model.
- The usual F-statistic does not appear in the output because this statistic is for testing the hypothesis that there is no linear relationship between the dependent variable and the (non-constant) regressors, and here the relationship is non-linear.
- The reported coefficient of determination (R-squared) could not fall if we added another regressor to the model.
- None of the above.