319,126 research outputs found
Exploring local dependence
This paper discusses two graphical methods for the investigation of local association of two continuous random variables. Often, scalar dependence measures, such as correlation, cannot reflect the complex dependence structure of two variables. However, dependence graphs have the potential to assess a far richer class of bivariate dependence structures. The two graphical methods discussed in this article are the chi-plot and the local dependence map. After the introduction of these methods they are applied to different data sets. These data sets contain simulated data and daily stock return series. With these examples the application possibilities of the two local dependence graphs are shown.Association, bivariate distribution, chi-plot, copula, correlation, kernel smoothing, local dependence, permutation test
Limit Theorems for Network Dependent Random Variables
This paper is concerned with cross-sectional dependence arising because
observations are interconnected through an observed network. Following Doukhan
and Louhichi (1999), we measure the strength of dependence by covariances of
nonlinearly transformed variables. We provide a law of large numbers and
central limit theorem for network dependent variables. We also provide a method
of calculating standard errors robust to general forms of network dependence.
For that purpose, we rely on a network heteroskedasticity and autocorrelation
consistent (HAC) variance estimator, and show its consistency. The results rely
on conditions characterized by tradeoffs between the rate of decay of
dependence across a network and network's denseness. Our approach can
accommodate data generated by network formation models, random fields on
graphs, conditional dependency graphs, and large functional-causal systems of
equations
Walk entropies on graphs
Entropies based on walks on graphs and on their line-graphs are defined. They are based on the summation over diagonal and off-diagonal elements of the thermal Green’s function of a graph also known as the communicability. The walk entropies are strongly related to the walk regularity of graphs and line-graphs. They are not biased by the graph size and have significantly better correlation with the inverse participation ratio of the eigenmodes of the adjacency matrix than other graph entropies. The temperature dependence of the walk entropies is also discussed. In particular, the walk entropy of graphs is shown to be non-monotonic for regular but non-walk-regular graphs in contrast to non-regular graphs
Testing bounded arboricity
In this paper we consider the problem of testing whether a graph has bounded
arboricity. The family of graphs with bounded arboricity includes, among
others, bounded-degree graphs, all minor-closed graph classes (e.g. planar
graphs, graphs with bounded treewidth) and randomly generated preferential
attachment graphs. Graphs with bounded arboricity have been studied extensively
in the past, in particular since for many problems they allow for much more
efficient algorithms and/or better approximation ratios.
We present a tolerant tester in the sparse-graphs model. The sparse-graphs
model allows access to degree queries and neighbor queries, and the distance is
defined with respect to the actual number of edges. More specifically, our
algorithm distinguishes between graphs that are -close to having
arboricity and graphs that -far from having
arboricity , where is an absolute small constant. The query
complexity and running time of the algorithm are
where denotes
the number of vertices and denotes the number of edges. In terms of the
dependence on and this bound is optimal up to poly-logarithmic factors
since queries are necessary (and .
We leave it as an open question whether the dependence on can be
improved from quasi-polynomial to polynomial. Our techniques include an
efficient local simulation for approximating the outcome of a global (almost)
forest-decomposition algorithm as well as a tailored procedure of edge
sampling
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