Fixed Point Theorems by D. R. Smart

By D. R. Smart

Show description

Read or Download Fixed Point Theorems PDF

Similar econometrics books

Stochastic Limit Theory: An Introduction for Econometricicans (Advanced Texts in Econometrics)

This significant new econometrics textual content surveys fresh advancements within the speedily increasing box of asymptotic distribution conception, with a distinct emphasis at the difficulties of time dependence and heterogeneity. Designed for econometricians and complicated scholars with constrained mathematical education, the ebook basically lays out the mandatory math and chance conception and makes use of various examples to make its information worthwhile and understandable.

Forecasting Non-Stationary Economic Time Series

Economies evolve and are topic to unexpected shifts brought about through legislative adjustments, monetary coverage, significant discoveries, and political turmoil. Macroeconometric versions are a really imperfect instrument for forecasting this hugely advanced and altering strategy. Ignoring those elements ends up in a large discrepancy among concept and perform.

Economics of Insurance

The speculation of assurance is gifted during this e-book, mentioned from the point of view of the speculation of economics of uncertainty. the primary of top rate calculation which the e-book makes use of relies on fiscal equilibrium idea and differs from some of the top class structures mentioned through actuaries. Reinsurance is built within the framework of common monetary equilibrium conception below uncertainty.

Econometrics

This is often an excerpt from the 4-volume dictionary of economics, a reference e-book which goals to outline the topic of economics this day. 1300 topic entries within the whole paintings conceal the huge topics of monetary idea. This extract concentrates on econometrics.

Extra resources for Fixed Point Theorems

Example text

P1: GEM/IKJ P2: GEM/IKJ QC: GEM/ABE CB495-03Drv CB495/Train KEY BOARDED 48 T1: GEM August 20, 2002 12:14 Char Count= 0 Behavioral Models The limitation of the logit model arises when we attempt to allow tastes to vary with respect to unobserved variables or purely randomly.

This probability is a J-dimensional integral over the density of the J error terms in εn = εn1 , . . , εn J . The dimension can be reduced, however, through recognizing that only differences in utility matter. With J errors (one for each alternative), there are J − 1 error differences. The choice probability can be expressed as a (J − 1)-dimensional integral over the density of these error differences: Pni = Prob(Uni > Un j ∀ j = i) = Prob(εn j − εni < Vni − Vn j ∀ j = i) = Prob(ε˜n ji < Vni − Vn j ∀ j = i) = I (ε˜n ji < Vni − Vn j ∀ j = i)g(ε˜ni ) d ε˜ni P1: GEM/IKJ P2: GEM/IKJ QC: GEM/ABE CB495-02Drv CB495/Train KEY BOARDED T1: GEM September 18, 2002 11:15 Char Count= 0 Properties of Discrete Choice Models 27 where ε˜n ji = εn j − εni is the difference in errors for alternatives i and j; ε˜ni = ε˜n1i , .

The variance of each error difference depends on the variances and covariances of the original errors. For example, the variance of the difference between the first and second errors is Var(ε˜n21 ) = Var(εn2 − εn1 ) = Var(εn1 ) + Var(εn2 ) − 2 Cov(εn1 , εn2 ) = σ11 + σ22 − 2σ12 . We can similarly calculate the covariance between ε˜n21 , which is the difference between the first and second errors, and ε˜n31 , which is the difference between the first and third errors: Cov(ε˜n21 , ε˜n31 ) = E(εn2 − εn1 )(εn3 − εn1 ) = E(εn2 εn3 − εn2 εn1 − εn3 εn1 + εn1 εn1 ) = σ23 − σ21 − σ31 + σ11 .

Download PDF sample

Rated 4.24 of 5 – based on 22 votes