3.4 Kindly help in answering

1. Suppose one has a random sample of n observations from the linear regression model Is the nonparametric bootstrap valid or invalid in the presence of heteroskedasticity? Explain. 2. Let the model be but E [ex] * 0, i.e. the regressors are endogenous. The OLS estimator A of the parameter 8 is biased. We know that the bootstrap is a good way to estimate bias, so the idea is to estimate the bias of # and construct a bias-adjusted estimate of 8. Explain whether or not the non-parametric bootstrap can be used to implement this idea. 3. Take the linear regression y=ofte, Belx] =0. For a particular value of r, the object of interest is the conditional mean g(x) = Elyx]. Describe how you would use the percentile-t bootstrap to construct a confidence interval for g(x)