STAT231 Lecture : chapter4d_CI_likelihood.pdf
17 Jan 2014
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Outline: chi squared distribution, confidence intervals from likelihoods. Chi squared distribution: goal: construct confidence intervals using likelihood, this will require the sampling distribution of the likelihood ratio, the sampling distribution is a new distribution that we now introduce. Chi squared distribution: the chi squared distribution is the distribution for this sum. G (0,1) independently: the sum has p summands, and p is also called the degrees of freedom , this distribution is frequently needed in praxis. Chi squared distribution: for p=2 , we have. 2: where each of the two variates are g(0,1, this is the squared (euclidean) distance from the origin of points generated from the 2- dimensional distribution. 20 stata: chidemo 50 (after loading package chidemo) Chi squared distribution: sum of two 2 distributions. Interval estimates: a point estimate of is a single value. 1 n i y i: an interval estimate of is an interval which (hopefully) contains .
