Consider the value that maximizes a function L( ). Let 0 denote an initial guess.
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Consider the value β̂ that maximizes a function L( β). Let β0 denote an initial guess.
a. Using L’( β̂.) = L’( β(0) + (β̂ – β(0) L”(β(0)) + ..., argue that for β(0) close to β̂, approximately 0 = L’( β(0)) + (β̂ – β(0)) L’’(β(0)).
Solve this equation to obtain an approximation β(1) for β̂.
b. Let β(t) denote approximation t for β̂, t = 0, 1, 2, ... Justify that the next approximation is β(t + 1) = β(t) – L’(β(t))/L”(β(t)).
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a Note ML estimate satisfies L 0 so dropping higherorder terms in ...View the full answer
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