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Lecture# Extreme Value Models: Technical Derivation

Description

This lecture covers the technical derivation of Multivariate Extreme Value models, focusing on the generating function and key technical conditions such as the limit property, u-homogeneity property, and strong alternating sign property. The lecture also explains how the model is derived from first principles, the motivation behind the technical conditions, and the properties of the model including marginal distributions, variance-covariance matrix, normalization, and the expected Maximum Utility. Additionally, it introduces the Inheritance theorem and highlights that Logit and nested Logit are part of the Multivariate Extreme Value family.

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In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. It was noted in various quite different settings that a short exact sequence often gives rise to a "long exact sequence". The concept of derived functors explains and clarifies many of these observations. Suppose we are given a covariant left exact functor F : A → B between two A and B.

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