Answer these questions 3.3 3.4

Please be thorough. Thankyou

1. Suppose one has a random sample of n observations from the linear regression model y=I$+n EM= Is the nonparametric bootstrap valid or invalid. in the presence of heteroslnedaaticity? Explain. 2. Let the model be t=f+e but E[e:r] 9': . i.e. the regressors are endogenous. The GL5 estimator ,6 of the parameter is biased. We knour that the bootstrap is a good way to estimate bias, so the idea is to estimate the bias of ,8 and construct a bias-adjusted estimate of 13. Explain whether or not the non-parametric bootstrap can be used to implement this idea. 3. Take the linear regression. y = :r'+e, E[e|:c] = i}. For a particular value of :r, the object of interest is the conditional mean 9(1) = EMI]. Describe how you would use the percentile-t bootstrap to construct a condence interval for star]- 1. Consider a random variable a with mean /. A random sample {e;}" is available. One estimates / by a, and a' by a,,. Find out what the bootstrap bias corrected estimators of / and oz are. 2. Suppose we have a sample of two independent observations z1 = 0 and z2 = 3 from the same distribution. Let us be interested in E[z"] and (E[=]) which are natural to estimate by 23= 1(2 + 2) and #2 = (21 + 22)2. Compute the bootstrap-bias-corrected estimates of the quantities of interest