The sub algebra functor Sub A is faithful for Boolean algebras (Sub A •Sub B implies A • B, see D. Sachs [7] ), but it is not faithful for bounded distributive lattices or unbounded distributive lattices. The automorphism functor Aut A is highly unfaithful even for Boolean algebras. The endomorphism functor End A is the most faithful of all three. B. M. Schein [8] and K. D.' Magill [5] establis...

This paper studies the connections among quantile regression, the asymmetric Laplace distribution, maximum likelihood and maximum entropy. We show that the maximum likelihood problem is equivalent to the solution of a maximum entropy problem where we impose moment constraints given by the joint consideration of the mean and median. Using the resulting score functions we propose an estimator bas...

A stochastic simulation procedure is proposed in this papa for obtaining median unbiased (Mu) estimates in macroeconometric models. MU estimates are computed for lagged dependent variable (LDV) coefficients in 18 equations of a macroeconometric model. The 2SLS bias for a coefficient, defined as the difference between the 2SLS estimate and the MU estimate, is on average smaller in absolute value...

Median networks have been proposed as an improvement over trees in phylogenetic analysis. This paper argues that concept lattices represent essentially the same information as median networks but with the advantage that there is a larger FCA research community and a variety of available software tools. Therefore evolutionary analysis is an interesting new application domain for FCA.

We study the L1 median for locationally uncertain points with discrete distributions. That is, each point in a data set has a discrete probability distribution describing its location. The L1 median is a robust estimator, useful when there are outliers in the point set. However given the probabilistic nature of this data, there is a distribution describing the L1 median, not a single location. ...

A large population of citizens have single-peaked preferences over a one-dimensional convex policy space with independently and identically distributed ideal points. They are partitioned into disjoint constituencies C1, . . . , Cm. Collective decisions are determined either in a directly democratic fashion and the implemented policy XD corresponds to the ideal point of the (issue-specific) popu...

Bandelt, H.-J. and H.M. Mulder, Pseudo-median graphs are join spaces, Discrete Mathematics 109 (1992) 13-26. Median graphs are known to share a number of geometrica! properties with Euclidean space, as is testified by the fact that median graphs ale (c!osed) join spaces-the segments of the associated join space being the geodesic intervals of the graph. As is shown in this paper the median join...

57 As we have seen at the beginning of the Great Recession, the household sector of an economy played a central role in the financial (in)stability that developed after the bust of the housing bubble in the U.S.A. (see e.g. Acharya et al., 2009; Claessens et al., 2010). Debelle (2004) had already pointed out that it is the distribution of debt that needs to be analyzed to investigate the effect...

We introduce the notion of a coarse median on a metric space. This satisfies the axioms of a median algebra up to bounded distance. The existence of such a median on a geodesic space is quasi-isometry invariant, and so applies to finitely generated groups via their Cayley graphs. We show that asymptotic cones of such spaces are topological median algebras. We define a notion of rank for a coars...

In the median problem, we are given a distance or dissimilarity measure d, three genomes G1, G2, and G3, and we want to find a genome G (a median) such that the sum ∑ 3 i=1 d(G,Gi) is minimized. The median problem is a special case of the multiple genome rearrangement problem, where one wants to find a phylogenetic tree describing the most “plausible” rearrangement scenario for multiple species...