Why does the starting point problem pose a problem for tests

Why does the starting point problem pose a problem for tests on the basis of a likelihood ratio Why is Box Cox estimation biased and median-unbiased Give three examples of biased estimation and discuss what can be done it the bias in each case. Describe the simultaneous equation problem. What happens to OLS estimates in this context

Solution

2. Median regression is used increasingly in many different areas of applications. The usual median regression estimating equations are derived from minimizing the least absolute deviations (LAD). Because they are not a smooth function of the regression parameters, a solution is best obtained using a linear programming algorithm. As an alternative, the median regression parameters via Gaussian estimating equations after applying a Box-Cox transformation to both the outcome and the linear predictor is notably more efficient than the standard LAD estimator, albeit with an acknowledged loss of robustness.

4. Simultaneous equation model: The model in which there is a single dependent variable and one or more explanatory variables then the model is called a single equation model. On the other hand, a system of equations representing a set of relationships among variables or describing the joint dependence of variables is called simultaneous equation. In such models there are more than one equation one of the mutually or jointly dependent or endogenous variables.

OLS estimator is not appropriate in a simultaneous equation:

The OLS estimate method is not appropriate in a simultaneous equation model because one or more explanatory variables are correlated with the disturbance term in that equation & the estimator thus obtained are inconsistent. For this reason OLS method is not appropriate in a simultaneous equation model.