By George G. Judge, William E. Griffiths, R. Carter Hill, Helmut Lutkepohl, Tsoung-Chao Lee
This widely established graduate-level textbook covers the most important types and statistical instruments at the moment utilized in the perform of econometrics. It examines the classical, the choice conception, and the Bayesian techniques, and comprises fabric on unmarried equation and simultaneous equation econometric types. contains an in depth reference checklist for every subject.
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Extra info for The Theory and Practice of Econometrics, Second Edition (Wiley Series in Probability and Statistics)
Robustness as a Criterion for Selecting a Probability Distribution . . 53 In many cases, it makes sense to limit ourselves to connected sets. In the 1-D case, the only connected sets are intervals [x, x] (finite or infinite). , it corresponds to checking whether x is larger than or equal to a certain lower threshold x and/or checking whether x is smaller than or equal to a certain upper threshold x, or to checking whether x belongs to the given tolerance interval [x, x]. From this viewpoint, all we need is for different intervals [x, x], to find the probability that the value x belongs to this interval.
I . We obtain empirical estimate E(I ) [h(Θ1:t )| X 1:t ] = (i) (i) I i=1 h(Θ1:t )wt (Θ1:t ) (i) I 1 i=1 wt (Θ1:t ) I 1 I I (i) h(Θ1:t ) = i=1 (i) ) wt (Θ1:t I j=1 ( j) wt (Θ1:t ) (12) . This importance sampling algorithm proposes to evaluate the function h under the empirical (discrete) distribution I π (I ) (θ1:t | X 1:t , θ0 ) = (i) Wt (Θ1:t ) δΘ (i) (θ1:t ) , 1:t i=1 with normalized importance weights (i) ) Wt (Θ1:t = (i) ) wt (Θ1:t I j=1 ( j) wt (Θ1:t ) = (i) (i) γt Θ1:t /qt (Θ1:t ) I j=1 ( j) ( j) γt Θ1:t /qt (Θ1:t ) .
25 is comparably small). The first observation 46 M. Wüthrich Fig. 25: (lhs) estimates and (rhs) resulting differences to the true sample Θ1:t ; the approximation on the (lhs) uses (27) with SMC and it is almost identically equal to the original SMC estimate (and therefore not visible in the plot) Fig. 11 Comparison between the true sample Θ1:t , the SIS estimate and the SMC estimate in the stochastic volatility model (23)–(24) for σ = 10: (lhs) estimates and (rhs) resulting differences to the true sample Θ1:t ; the approximation on the (lhs) uses (26) is that we cannot distinguish the SMC results from models (24) and (27), thus, our de-trending term is too small to be helpful to improve inference of the transition system.