Let B be an n-dimensional random vector of zero mean and positive- definite covariance matrix Q. Suppose measurements of the form y = WB are made where the rank of W is m. If B is the linear
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- Given that the σ_AB= σ_BA, then the variance-covariance matrix for a portfolio with 50 stocks requires the calculations of ____ variances and ____ covariances.Describe each of the five “Gauss Markov” assumptions, (define them) and explain in the context of the regression outputif only given a column vector function (2x1), f(B) = [e^(B1) - 1 ; e^(B2) - 1], then how do you find the asymptotic variance-covariance matrix estimator using the Delta method?
- In the simple linear regression model , the Gauss Markov ( classical ) assumptions guarantee that the OLS estimator of the unknown parameters is BLUE. Among those assumptions , in order to have consistency of the OLS estimator we need ( this is a question on the necessary condition ): Question 4Select one: a. we need that the errors are not correlated with each others and that they have zero mean b. we need that the errors are homoscedastic ( all have the same variance) c. we need that the residuals are not correlated with the explanatory variables and that the residuals have zero mean d. we need that the errors have zero mean and that they are not correlated with the regressors ( no endogeneity) e. we need that the errors are homoscedastic ( all have the same variance) and not correlated with each others ( no serial correlation)Suppose A is an m x mateix whose columns are linearly independent. What is the nullity of A?Find the OLS estimators for the parameters using the matrices above.
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- The following are some applications of the Markovinequality of Exercise 29:(a) The scores that high school juniors get on the verbalpart of the PSAT/NMSQT test may be looked upon asvalues of a random variable with the mean μ = 41. Findan upper bound to the probability that one of the studentswill get a score of 65 or more.(b) The weight of certain animals may be looked uponas a random variable with a mean of 212 grams. If noneof the animals weighs less than 165 grams, find an upperbound to the probability that such an animal will weigh atleast 250 grams.Let X1, ..., X20 be independent Poisson random variables with mean one. 1 2 (a) Use the Markov inequality to obtain a bound on P (X1 + X2 + · · · + X20 > 15). (b) Use the central limit theorem to approximate the above probability.What are the difficulties in estimating the following model? Use as much detail as possible in answering this question while considering the Gauss-Markov assumptions and OLS estimator. Economic productivity = β0 + β1Unemployment + β2Innovation + θiControls + ei Where unemployment is the average unemployment rate of a country and innovation is an index of R&D performance.