Results 1  10
of
100
Large Sample Properties of Matching Estimators for Average Treatment Effects
 ECONOMETRICA 74,235267
, 2006
"... Matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases. The absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not ap ..."
Abstract

Cited by 318 (18 self)
 Add to MetaCart
Matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases. The absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data. In this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results. We focus on matching with replacement with a fixed number of matches. First, we show that matching estimators are not N1/2consistent in general and describe conditions under which matching estimators do attain N1/2consistency. Second, we show that even in settings where matching estimators are N1/2consistent, simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound. Third, we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions. Software for implementing these methods is available in Matlab, Stata, and R.
Spectral partitioning works: planar graphs and finite element meshes, in:
 Proceedings of the 37th Annual Symposium on Foundations of Computer Science,
, 1996
"... Abstract Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to wo ..."
Abstract

Cited by 201 (10 self)
 Add to MetaCart
(Show Context)
Abstract Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on boundeddegree planar graphs and finite element meshesthe classes of graphs to which they are usually applied. While naive spectral bisection does not necessarily work, we prove that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is O( √ n) for boundeddegree planar graphs and twodimensional meshes and O(n 1/d ) for wellshaped ddimensional meshes. The heart of our analysis is an upper bound on the secondsmallest eigenvalues of the Laplacian matrices of these graphs: we prove a bound of O(1/n) for boundeddegree planar graphs and O(1/n 2/d ) for wellshaped ddimensional meshes.
An Analysis of Recent Work on Clustering Algorithms
, 1999
"... This paper describes four recent papers on clustering, each of which approaches the clustering problem from a different perspective and with different goals. It analyzes the strengths and weaknesses of each approach and describes how a user could could decide which algorithm to use for a given clust ..."
Abstract

Cited by 86 (0 self)
 Add to MetaCart
This paper describes four recent papers on clustering, each of which approaches the clustering problem from a different perspective and with different goals. It analyzes the strengths and weaknesses of each approach and describes how a user could could decide which algorithm to use for a given clustering application. Finally, it concludes with ideas that could make the selection and use of clustering algorithms for data analysis less difficult.
Models and Approximation Algorithms for Channel Assignment in Radio Networks
, 2000
"... We consider the frequency assignment (broadcast scheduling) problem for packet radio networks. Such networks are naturally modeled by graphs with a certain geometric structure. The problem of broadcast scheduling can be cast as a variant of the vertex coloring problem (called the distance2 coloring ..."
Abstract

Cited by 84 (3 self)
 Add to MetaCart
(Show Context)
We consider the frequency assignment (broadcast scheduling) problem for packet radio networks. Such networks are naturally modeled by graphs with a certain geometric structure. The problem of broadcast scheduling can be cast as a variant of the vertex coloring problem (called the distance2 coloring problem) on the graph that models a given packet radio network. We present efficient approximation algorithms for the distance2 coloring problem for various geometric graphs including those that naturally model a large class of packet radio networks. The class of graphs considered include (r, s)civilized graphs, planar graphs, graphs with bounded genus, etc.
APPROXIMATING CENTER POINTS WITH ITERATIVE Radon Points
 INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS
, 1995
"... ..."
(Show Context)
PolynomialTime Approximation Schemes for Packing and Piercing Fat Objects
 JOURNAL OF ALGORITHMS
, 2001
"... We consider two problems: given a collection of n fat objects in a xed dimension, 1. (packing) nd the maximum subcollection of pairwise disjoint objects, and 2. (piercing) nd the minimum point set that intersects every object. Recently, Erlebach, Jansen, and Seidel gave a polynomialtime approxim ..."
Abstract

Cited by 50 (5 self)
 Add to MetaCart
(Show Context)
We consider two problems: given a collection of n fat objects in a xed dimension, 1. (packing) nd the maximum subcollection of pairwise disjoint objects, and 2. (piercing) nd the minimum point set that intersects every object. Recently, Erlebach, Jansen, and Seidel gave a polynomialtime approximation scheme (PTAS) for the packing problem, based on a shifted hierarchical subdivision method. Using shifted quadtrees, we describe a similar algorithm for packing but with a smaller time bound. Erlebach et al.'s algorithm requires polynomial space. We describe a dierent algorithm, based on geometric separators, that requires only linear space. This algorithm can also be applied to piercing, yielding the rst PTAS for that problem. Abbreviated title. Packing and Piercing Fat Objects.
RelationshipBased Clustering and Visualization for HighDimensional Data Mining
 INFORMS Journal on Computing
, 2002
"... In several reallife datamining... This paper proposes a relationshipbased approach that alleviates both problems, sidestepping the "curseofdimensionality" issue by working in a suitable similarity space instead of the original highdimensional attribute space. This intermediary simil ..."
Abstract

Cited by 44 (10 self)
 Add to MetaCart
(Show Context)
In several reallife datamining... This paper proposes a relationshipbased approach that alleviates both problems, sidestepping the "curseofdimensionality" issue by working in a suitable similarity space instead of the original highdimensional attribute space. This intermediary similarity space can be suitably tailored to satisfy business criteria such as requiring customer clusters to represent comparable amounts of revenue. We apply efficient and scalable graphpartitioningbased clustering techniques in this space. The output from the clustering algorithm is used to reorder the data points so that the resulting permuted similarity matrix can be readily visualized in two dimensions, with clusters showing up as bands. While twodimensional visualization of a similarity matrix is by itself not novel, its combination with the ordersensitive partitioning of a graph that captures the relevant similarity measure between objects provides three powerful properties: (i) the highdimensionality of the data does not affect further processing once the similarity space is formed; (ii) it leads to clusters of (approximately) equal importance, and (iii) related clusters show up adjacent to one another, further facilitating the visualization of results. The visualization is very helpful for assessing and improving clustering. For example, actionable recommendations for splitting or merging of clusters can be easily derived, and it also guides the user toward the right number of clusters
Compact Representations of Separable Graphs
 In Proceedings of the Annual ACMSIAM Symposium on Discrete Algorithms
, 2003
"... We consider the problem of representing graphs compactly while supporting queries e#ciently. In particular we describe a data structure for representing nvertex unlabeled graphs that satisfy an O(n )separator theorem, c < 1. The structure uses O(n) bits, and supports adjacency and degree qu ..."
Abstract

Cited by 42 (11 self)
 Add to MetaCart
(Show Context)
We consider the problem of representing graphs compactly while supporting queries e#ciently. In particular we describe a data structure for representing nvertex unlabeled graphs that satisfy an O(n )separator theorem, c < 1. The structure uses O(n) bits, and supports adjacency and degree queries in constant time, and neighbor listing in constant time per neighbor. This generalizes previous results for graphs with constant genus, such as planar graphs.
Map Labeling and Its Generalizations
"... Map labeling is of fundamental importance in cartography and geographical information systems and is one of the areas targeted for research by the ACM Computational Geometry Impact Task Force. Previous work on map labeling has focused on the problem of placing maximal uniform, axisaligned, disjoint ..."
Abstract

Cited by 41 (5 self)
 Add to MetaCart
Map labeling is of fundamental importance in cartography and geographical information systems and is one of the areas targeted for research by the ACM Computational Geometry Impact Task Force. Previous work on map labeling has focused on the problem of placing maximal uniform, axisaligned, disjoint rectangles on the plane so that each point feature to be labeled lies at the corner of one rectangle. Here, we consider a number of variants of the map labeling problem. We obtain three general types of results. First, we devise constantfactor polynomialtime approximation algorithms for labeling point features by rectangular labels, where the feature may lie anywhere on the boundary of its label region and where labeling rectangles may be placed in any orientation. These results generalize to the case of elliptical labels. Secondly, we consider the problem of labeling a map consisting of disjoint rectilinear line segments. We obtain constantfactor polynomialtime approximation algorithms for the general problem and an optimal algorithm for the special case where all segments are horizontal. Finally, we formulate a bicriteria version of the maplabeling problem and provide bicriteria polynomialtime approximation schemes for a number of such problems.