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Toward Simplifying and Accurately Formulating Fragment Assembly
 JOURNAL OF COMPUTATIONAL BIOLOGY
, 1995
"... The fragment assembly problem is that of reconstructing a DNA sequence from a collection of randomly sampled fragments. Traditionally the objective of this problem has been to produce the shortest string that contains all the fragments as substrings, but in the case of repetitive target sequence ..."
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Cited by 37 (1 self)
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The fragment assembly problem is that of reconstructing a DNA sequence from a collection of randomly sampled fragments. Traditionally the objective of this problem has been to produce the shortest string that contains all the fragments as substrings, but in the case of repetitive target sequences this objective produces answers that are overcompressed. In this paper, the problem is reformulated as one of finding a maximumlikelihood reconstruction with respect to the 2sided KolmogorovSmirnov statistic, and it is argued that this is a better formulation of the problem. Next the fragment assembly problem is recast in graphtheoretic terms as one of finding a noncyclic subgraph with certain properties and the objectives of being shortest or maximallylikely are also recast in this framework. Finally, a series of graph reduction transformations are given that dramatically reduce the size of the graph to be explored in practical instances of the problem. This reduction is ...
An L p view of the BahadurKiefer theorem
"... 56> kR n k p = p kff n k (p=2) converges almost surely to a finite positive explicit constant. We also extend our result to a more general BahadurKiefer process. Keywords. Empirical process, quantile process, BahadurKiefer representation, L p  modulus of continuity for Brownian motion, Br ..."
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Cited by 2 (2 self)
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56> kR n k p = p kff n k (p=2) converges almost surely to a finite positive explicit constant. We also extend our result to a more general BahadurKiefer process. Keywords. Empirical process, quantile process, BahadurKiefer representation, L p  modulus of continuity for Brownian motion, Brownian bridge, Kiefer process. 1991 Mathematics Subject Classification. Primary 60F25; Secondary 62G30. Research supported by an NSERC Canada Grant at Carleton University, Ottawa, and by a Paul Erdos Visiting Professorship of the Paul Erdos Summer Research Center of Mathematics, Budapest. Research supported by a Fellowship of the Paul Erdos Summer Research Center of Mathematics, Budapest.  1  1. Introduction Let fU i g<F48.69
MAXIMA OF ASYMPTOTICALLY GAUSSIAN RANDOM FIELDS AND MODERATE DEVIATION APPROXIMATIONS TO BOUNDARYCROSSING PROBABILITIES OF SUMS OF RANDOM VARIABLES WITH MULTIDIMENSIONAL INDICES
, 2004
"... Several classical results on boundarycrossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices, multivariate empirical processes, and scan statistics in changepoint a ..."
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Cited by 2 (0 self)
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Several classical results on boundarycrossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices, multivariate empirical processes, and scan statistics in changepoint and signal detection as special cases. Some key ingredients in these extensions are moderate deviation approximations to marginal tail probabilities and weak convergence of the conditional distributions of certain “clumps” around highlevel crossings. We also discuss how these results are related to the Poisson clumping heuristic and tube formulas of Gaussian random fields, and describe their applications to laws of the iterated logarithm in the form of the Kolmogorov–Erdős–Feller integral tests.
BOUNDARY KERNELS FOR DISTRIBUTION FUNCTION ESTIMATION Author:
, 2012
"... Boundary effects for kernel estimators of curves with compact supports are well known in regression and density estimation frameworks. In this paper we address the use of boundary kernels for distribution function estimation. We establish the ChungSmirnov law of iterated logarithm and an asymptotic ..."
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Cited by 1 (1 self)
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Boundary effects for kernel estimators of curves with compact supports are well known in regression and density estimation frameworks. In this paper we address the use of boundary kernels for distribution function estimation. We establish the ChungSmirnov law of iterated logarithm and an asymptotic expansion for the mean integrated squared error of the proposed estimator. These results show the superior theoretical performance of the boundary modified kernel estimator over the classical kernel estimator for distribution functions that are not smooth at the extreme points of the distribution support. The automatic selection of the bandwidth is also briefly discussed in this paper. Beta reference distribution and crossvalidation bandwidth selectors are considered. Simulations suggest that the crossvalidation bandwidth performs well, although the simpler reference distribution bandwidth is quite effective for the generality of test distributions. KeyWords: kernel distribution function estimation; boundary kernels; ChungSmirnov property; MISE expansion; bandwidth selection. AMS Subject Classification: • 62G05, 62G20. 170 Carlos TenreiroBoundary kernels for distribution function estimation 171
THE ASYMPTOTIC POWER OF THE KOIMOGOROV TESTS OF GOODNESS OF FIT
, 1959
"... The asymptotic power of the onesided and twosided Kolmogorov tests of goodness of fit of a hypothesis distribution H(x) against sequences of alternatives Gn(x) for 'which s ~ JnIH(x)Gn(x)I tends to a limit is investigated by application of Doobls "heuristic procedure"; bounds on the power are fo ..."
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The asymptotic power of the onesided and twosided Kolmogorov tests of goodness of fit of a hypothesis distribution H(x) against sequences of alternatives Gn(x) for 'which s ~ JnIH(x)Gn(x)I tends to a limit is investigated by application of Doobls "heuristic procedure"; bounds on the power are found, and some numerical examples provided.
Key words and phrases. Brownian bridge, rescaling, excursions, extrema,
, 2009
"... Abstract. Functionals of Brownian bridge arise as limiting distributions in nonparametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. Only the Poisson character of the excursion process will be ..."
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Abstract. Functionals of Brownian bridge arise as limiting distributions in nonparametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. Only the Poisson character of the excursion process will be used. Particular cases of calculations include the distributions of the KolmogorovSmirnov statistic, the Kuiper statistic, and the ratio of the maximum positive ordinate to the minumum negative ordinate.
Reliability and robustness of rainfall compound distribution model
, 2011
"... www.hydrolearthsystsci.net/15/519/2011/ ..."
Uncertainty Quantification Using ConcentrationofMeasure Inequalities
, 2009
"... This work introduces a rigorous uncertainty quantification framework that exploits concentration–of–measure inequalities to bound failure probabilities using a welldefined certification campaign regarding the performance of engineering systems. The framework is constructed to be used as a tool for ..."
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This work introduces a rigorous uncertainty quantification framework that exploits concentration–of–measure inequalities to bound failure probabilities using a welldefined certification campaign regarding the performance of engineering systems. The framework is constructed to be used as a tool for deciding whether a system is likely to perform safely and reliably within design specifications. Concentrationofmeasure inequalities rigorously bound probabilitiesoffailure and thus supply conservative certification criteria, in addition to supplying unambiguous quantitative definitions of terms such as margins, epistemic and aleatoric uncertainties, verification and validation measures, and confidence factors. This methodology unveils clear procedures for computing the latter quantities by means of concerted simulation and experimental campaigns. Extensions to the theory include hierarchical uncertainty quantification, and validation with experimentally uncontrollable random variables. v Acknowledgments