Methods explained: Index numbers

Geometry of Numbers Explained

Sums of Squares Methods Explained: Part I

Let p(~x) ∈ R[~x] be SOS in t real polynomial squares. Then, p(~x) must have even degree. Let deg(p(~x)) = 2k. Then, ∃q1, . . . , qt ∈ R[~x] s.t. deg(qi(~x)) ≤ k and p(~x) = ∑t i=1 q 2 i (~x). A key observation is that we can now exactly characterise the finitely many possible power-products that could occur in each qi(~x). Definition 1.1. Let Λn(d) = {α = 〈α1, . . . , αn〉 ∈ Nn | α1 + . . .+ αn...

CREDIBILITY THEORY ORIENTED PREFERENCE INDEX FOR RANKING FUZZY NUMBERS

This paper suggests  a novel approach for ranking the most applicable fuzzy numbers, i.e.  $LR$-fuzzy numbers. Applying the  $alpha$-optimistic values of a fuzzy number, a preference criterion is proposed for ranking fuzzy numbers using the Credibility index. The main properties of the proposed  preference criterion  are also studied.  Moreover, the proposed method is   applied for ranking fuzz...

Monetary Aggregation Theory and Statistical Index Numbers

This paper is the first of two from the Monetary Services Indices (MSI) Project at the Federal Reserve Bank ofSt. Louis. The second paper, Working Paper 96-008B, summarizes the methodology, construction and data sourcesfor the an extensive new database of monetary services indices, often referred to as Divisia monetary aggregates, for the United States. This paper surveys the microeconomic theo...

On the Stochastic Approach to Index Numbers