Question

Consider the following linear regression model 1. For any X x, let Y xBU, where 3 E R*. 2. X is exogenous 3. The probability model is {f(u;0) is a distribution on R: Ef [U] = 0, VAR, [U] = 02,0 > 0}. 4. Sampling model: Y} anidependent sample, sequentially generated using Yi x Ui,where the U IID(0,0) are (i) Let K 0 be a given number. We wish to estimate B using least-squares subject to the constraint 6BK2. Write down the Lagrangian for this optimization problem. Show all of your derivations (ii) What is the constraint qualification for this problem ? Does this optimization problem satisfy it? If so, then what is its consequence ? Explain your answers (ii What are the Karush-Kuhn-Tucker conditions for this optimization problem. Explain your answer (iv) Compute the optimal solution of this optimization problem. Show all of your derivations

Answer 1

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