STA305H1 Lecture Notes - Lecture 5: Location Parameter, Likelihood Function, Poisson Distribution
18 Jan 2018
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Document Summary
The newton-raphson algorithm: computing the mle of the cauchy distribution. The newton-raphson algorithm is a general purpose method for solving equations of the form g(x ) = 0 where g(x) is a (non-linear) di erentiable function with derivative g (x). This algorithm solves for x by computing successive approximations x(1), x(2), via the formula x(k) = x(k 1) + g(x(k 1)) g (x(k 1)) The success of the newton-raphson algorithm depends on the choice of an initial estimate x(0). A natural application of the newton-raphson algorithm is the computation of maximum likelihood estimates (mles). Suppose that is a real-valued parameter lying in a open parameter space ; if lnl( ) is the log-likelihood function and s( ) is its derivative with respect to then the mle b satis es the likelihood equation. I(b (k 1)) where i( ) = s ( ); note that i(b ) is simply the observed fisher information.
