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TreeValued Markov Chains Derived From GaltonWatson Processes.
 Ann. Inst. Henri Poincar'e
, 1997
"... Let G be a GaltonWatson tree, and for 0 u 1 let G u be the subtree of G obtained by retaining each edge with probability u. We study the treevalued Markov process (G u ; 0 u 1) and an analogous process (G u ; 0 u 1) in which G 1 is a critical or subcritical GaltonWatson tree conditio ..."
Abstract

Cited by 57 (9 self)
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Let G be a GaltonWatson tree, and for 0 u 1 let G u be the subtree of G obtained by retaining each edge with probability u. We study the treevalued Markov process (G u ; 0 u 1) and an analogous process (G u ; 0 u 1) in which G 1 is a critical or subcritical GaltonWatson tree conditioned to be infinite. Results simplify and are further developed in the special case of Poisson() offspring distribution. Running head. Treevalued Markov chains. Key words. Borel distribution, branching process, conditioning, GaltonWatson process, generalized Poisson distribution, htransform, pruning, random tree, sizebiasing, spinal decomposition, thinning. AMS Subject classifications 05C80, 60C05, 60J27, 60J80 Research supported in part by N.S.F. Grants DMS9404345 and 9622859 1 Contents 1 Introduction 2 1.1 Related topics : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2 Background and technical setup 5 2.1 Notation and terminology for trees : : : : : : : : : : : : : : :...
Monte Carlo test methods in econometrics
 Companion to Theoretical Econometrics’, Blackwell Companions to Contemporary Economics
, 2001
"... The authors thank three anonymous referees and the Editor Badi Baltagi for several useful comments. This work was supported by the Bank of Canada and by grants from the Canadian Network of Centres of Excellence [program on Mathematics ..."
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Cited by 35 (24 self)
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The authors thank three anonymous referees and the Editor Badi Baltagi for several useful comments. This work was supported by the Bank of Canada and by grants from the Canadian Network of Centres of Excellence [program on Mathematics
The Statistical Significance of Canonical Correlations
 Biometrika
, 1941
"... shown that the generalized variance matrix* of a vector variate x which has been partitioned into two parts x1 and Xj with, say, q and p components, can, by appropriate linear transformations LxXj and L2x2 of xx and Xj, be thrown into the canonical form ..."
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Cited by 16 (0 self)
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shown that the generalized variance matrix* of a vector variate x which has been partitioned into two parts x1 and Xj with, say, q and p components, can, by appropriate linear transformations LxXj and L2x2 of xx and Xj, be thrown into the canonical form
On the distribution of ranked heights of excursions of a Brownian bridge
 In preparation
, 1999
"... The distribution of the sequence of ranked maximum and minimum values attained during excursions of a standard Brownian bridge (B br t ; 0 t 1) is described. The height M br+ j of the jth highest maximum over a positive excursion of the bridge has the same distribution as M br+ 1 =j, where th ..."
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Cited by 15 (5 self)
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The distribution of the sequence of ranked maximum and minimum values attained during excursions of a standard Brownian bridge (B br t ; 0 t 1) is described. The height M br+ j of the jth highest maximum over a positive excursion of the bridge has the same distribution as M br+ 1 =j, where the distribution of M br+ 1 = sup 0t1 B br t is given by L'evy's formula P (M br+ 1 ? x) = e \Gamma2x 2 . The probability density of the height M br j of the jth highest maximum of excursions of the reflecting Brownian bridge (jB br t j; 0 t 1) is given by a modification of the known `function series for the density of M br 1 = sup 0t1 jB br t j. These results are obtained from a more general description of the distribution of ranked values of a homogeneous functional of excursions of the standardized bridge of a selfsimilar recurrent Markov process. Keywords: Brownian bridge, Brownian excursion, Brownian scaling, local time, selfsimilar recurrent Markov process, Bessel p...
Critical random graphs: limiting constructions and distributional properties
, 2010
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Asymptotic optimality of multicenter Voronoi configurations for random field estimation
 IEEE Transactions on Automatic Control
, 2008
"... This paper deals with multiagent networks performing optimal estimation tasks. Consider a network of mobile agents with sensors that can take measurements of a spatial process in an environment of interest. Using the measurements, one can construct a kriging interpolation of the spatial field over ..."
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Cited by 15 (5 self)
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This paper deals with multiagent networks performing optimal estimation tasks. Consider a network of mobile agents with sensors that can take measurements of a spatial process in an environment of interest. Using the measurements, one can construct a kriging interpolation of the spatial field over the whole environment, with an associated prediction error at each point. We study the continuity properties of the prediction error, and consider as global objective functions the maximum prediction error and the generalized prediction variance. We study the network configurations that give rise to optimal field interpolations. Specifically, we show how, as the correlation between any two different locations vanishes, circumcenter and incenter Voronoi configurations become network configurations that optimize the maximum prediction error and the generalized prediction variance, respectively. The technical approach draws on tools from geostatistics, computational geometry, linear algebra, and dynamical systems. I.
The Distribution of Local Times of a Brownian bridge,Sém
 Prob. XXXIII Lecture Notes in Mathematics 1709
, 1999
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OPTIMAL RANKBASED TESTING FOR PRINCIPAL COMPONENTS
"... This paper provides parametric and rankbased optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and their pseudoGaussian robustifications by Tyler (1981, 1983) a ..."
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Cited by 13 (11 self)
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This paper provides parametric and rankbased optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and their pseudoGaussian robustifications by Tyler (1981, 1983) and Davis (1977), with which their Gaussian versions are shown to coincide, asymptotically, under Gaussian or finite fourthorder moment assumptions, respectively. Such assumptions however restrict the scope to covariancebased principal component analysis. The rankbased tests we are proposing remain valid without such assumptions. Hence, they address a much broader class of problems, where covariance matrices need not exist and principal components are associated with more general scatter matrices. Asymptotic relative efficiencies moreover show that those rankbased tests are quite powerful; when based on van der Waerden or normal scores, they even uniformly dominate the pseudoGaussian versions
Applications of size biased couplings for concentration of measures
, 2010
"... Let Y be a nonnegative random variable with mean µ and finite positive variance σ2, and let Y s, defined on the same space as Y, have the Y size biased distribution, that is, the distribution characterized by E[Y f(Y)] = µEf(Y s) for all functions f for which these expectations exist. Under a varie ..."
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Cited by 13 (6 self)
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Let Y be a nonnegative random variable with mean µ and finite positive variance σ2, and let Y s, defined on the same space as Y, have the Y size biased distribution, that is, the distribution characterized by E[Y f(Y)] = µEf(Y s) for all functions f for which these expectations exist. Under a variety of conditions on the coupling of Y and Y s, including combinations of boundedness and monotonicity, concentration of measure inequalities such as P Y − µ