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41,134
Directional Statistics and Shape Analysis
, 1995
"... There have been various developments in shape analysis in the last decade. We describe here some relationships of shape analysis with directional statistics. For shape, rotations are to be integrated out or to be optimized over whilst they are the basis for directional statistics. However, various c ..."
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Cited by 794 (33 self)
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concepts are connected. In particular, certain distributions of directional statistics have emerged in shape analysis, such a distribution is Complex Bingham Distribution. This paper first gives some background to shape analysis and then it goes on to directional distributions and their applications
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
, 2010
"... ..."
Statistical Analysis of Cointegrated Vectors
 Journal of Economic Dynamics and Control
, 1988
"... We consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors. We then derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number of dimen ..."
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Cited by 2749 (12 self)
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of dimensions. Further we test linear hypotheses about the cointegration vectors. The asymptotic distribution of these test statistics are found and the first is described by a natural multivariate version of the usual test for unit root in an autoregressive process, and the other is a x2 test. 1.
Accurate Methods for the Statistics of Surprise and Coincidence
 COMPUTATIONAL LINGUISTICS
, 1993
"... Much work has been done on the statistical analysis of text. In some cases reported in the literature, inappropriate statistical methods have been used, and statistical significance of results have not been addressed. In particular, asymptotic normality assumptions have often been used unjustifiably ..."
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Cited by 1057 (1 self)
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Much work has been done on the statistical analysis of text. In some cases reported in the literature, inappropriate statistical methods have been used, and statistical significance of results have not been addressed. In particular, asymptotic normality assumptions have often been used
Powerlaw distributions in empirical data
 ISSN 00361445. doi: 10.1137/ 070710111. URL http://dx.doi.org/10.1137/070710111
, 2009
"... Powerlaw distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and manmade phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the t ..."
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Cited by 607 (7 self)
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in the tail of the distribution. In particular, standard methods such as leastsquares fitting are known to produce systematically biased estimates of parameters for powerlaw distributions and should not be used in most circumstances. Here we describe statistical techniques for making accurate parameter
Semantic similarity based on corpus statistics and lexical taxonomy
 Proc of 10th International Conference on Research in Computational Linguistics, ROCLING’97
, 1997
"... This paper presents a new approach for measuring semantic similarity/distance between words and concepts. It combines a lexical taxonomy structure with corpus statistical information so that the semantic distance between nodes in the semantic space constructed by the taxonomy can be better quantifie ..."
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Cited by 873 (0 self)
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This paper presents a new approach for measuring semantic similarity/distance between words and concepts. It combines a lexical taxonomy structure with corpus statistical information so that the semantic distance between nodes in the semantic space constructed by the taxonomy can be better
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 543 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain
Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images.
 IEEE Trans. Pattern Anal. Mach. Intell.
, 1984
"... AbstractWe make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a latticelike physical system. The assignment of an energy function in the physical system determines its Gibbs di ..."
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Cited by 5126 (1 self)
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AbstractWe make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a latticelike physical system. The assignment of an energy function in the physical system determines its Gibbs
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 783 (29 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We
Estimating the number of clusters in a dataset via the Gap statistic
, 2000
"... We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference ..."
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Cited by 502 (1 self)
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null distribution. Some theory is developed for the proposal and a simulation study that shows that the Gap statistic usually outperforms other methods that have been proposed in the literature. We also briey explore application of the same technique to the problem for estimating the number of linear
Results 1  10
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41,134