Construct the likelihood function L(0,A, σ 2) of: exp Where Yi-NG, + βί Xi, σ2) and estimate βο, βι and σ2 in Y-β0 + Axi + εϊ , where εί-N(0, σ2) ,using the MLE. Compare the least squares estimators...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distributed ran- dom variables with Ei ~ N (0,02), where σ2 is a third unknown pa- rameter. This is the familiar form for a simple linear regression model, where the parameters A, β, and σ2 explain the relationship between a dependent (or response) variable Y...
5 points Suppose that Yi N(0, σ ). Write out the likelihood for the data and show that it is equivalently to using ordinary least squares = β0 +너=12'ij8; + ei where ei, , en are iid. distributed from a 5 points Suppose that Yi N(0, σ ). Write out the likelihood for the data and show that it is equivalently to using ordinary least squares = β0 +너=12'ij8; + ei where ei, , en are iid. distributed from a
QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution, and let S2 and Š-n--S2 be two estimators of σ2. Given: E (S2) σ 2 and V (S2) - ya-X)2 n-l -σ (a) Determine: E S2): (l) V (S2); and (il) MSE (S) (b) Which of s2 and S2 has a larger mean square error? (c) Suppose thatnis an estimator of e based on a random sample of size n. Another equivalent definition of...