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Download e-book for iPad: Analysis of microdata : with 38 figures and 41 tables by Rainer Winkelmann; Stefan Boes

By Rainer Winkelmann; Stefan Boes

ISBN-10: 3540296050

ISBN-13: 9783540296058

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But this is not the usual procedure. The reason is that it is both difficult and unnecessary to specify a full joint model. It is difficult, because in more realistic set-ups there are many explanatory variables and parameters, and except for special cases (such as if X and Y are multivariate normally distributed) the derivations may become cumbersome and the integrals required may not even have a closed-form solution. It is unnecessary because one can start in many cases directly with a conditional model and leave the joint distribution completely unspecified.

1 Axioms of Probability To begin with, recall some elementary concepts from probability theory. , the set of all possible elementary outcomes ωi of an experiment, and call any subset of Ω an event A. In microdata applications, the fundamental experiment is a draw from the underlying population in order to measure the outcome of a variable. For example, the random draw could be from the set of all young men, in order to determine whether the selected male attends university or not. In this case, the sample space given by Ω = {not attending university, attending university}.

We see that if the expected score is evaluated at the true parameter θ0 , the f (yi ; θ0 )-expressions cancel and we obtain ∂f (yi ; θ) dyi ∂θ E[s(θ0 ; yi )] = =0 θ=θ0 The expected score for each single observation, if evaluated at the true parameter, is zero, which was to be shown. As a consequence, the expected score vector of the full sample is zero as well. 3. Sampling from a Bernoulli Distribution (Part III) Assume that a random sample of size n has been drawn from a Bernoulli distribution with true parameter π0 , as before.

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Analysis of microdata : with 38 figures and 41 tables by Rainer Winkelmann; Stefan Boes

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