Search results for " Bounds"

showing 10 items of 291 documents

A Distribution-Free Two-Sample Equivalence Test Allowing for Tied Observations

1999

A new testing procedure is derived which enables to assess the equivalence of two arbitrary noncontinuous distribution functions from which unrelated samples are taken as the data to be analyzed. The equivalence region is defined to consist of all pairs (F, G) of distribution functions such that for independent X ∼F, Y ∼G the conditional probability of {X > Y} given {X ¬= Y} lies in some short interval around 1/2. The test rejects the null hypothesis of nonequivalence if and only if the standardized distance between the U-statistics estimator of P|X > Y | X ¬= Y] and the center of the equivalence interval (1/2 - e 1 , 1/2 + e 2 ) does not exceed a critical upper bound which has to be comput…

Statistics and ProbabilityConditional probabilityEstimatorGeneral MedicineUpper and lower boundsCombinatoricsDelta methodDistribution functionSampling distributionStatisticsStatistics Probability and UncertaintyEquivalence (measure theory)MathematicsNoncentrality parameterBiometrical Journal
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Cotas inferiores para el QAP-Arbol

1985

The Tree-QAP is a special case of the Quadratic Assignment Problem where the flows not equal zero form a tree. No condition is required for the distance matrix. In this paper we present an integer programming formulation for the Tree-QAP. We use this formulation to construct four Lagrangean relaxations that produce several lower bounds for this problem. To solve one of the relaxed problems we present a Dynamic Programming algorithm which is a generalization of the algorithm of this type that gives a lower bound for the Travelling Salesman Problem. A comparison is given between the lower bounds obtained by each ralaxation for examples with size from 12 to 25.

Statistics and ProbabilityDynamic programmingCombinatoricsDistance matrixGeneralizationQuadratic assignment problemStatistics Probability and UncertaintySpecial caseUpper and lower boundsTravelling salesman problemInteger programmingMathematicsTrabajos de Estadistica y de Investigacion Operativa
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Can the Adaptive Metropolis Algorithm Collapse Without the Covariance Lower Bound?

2011

The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix at step $n+1$ \[ S_n = Cov(X_1,...,X_n) + \epsilon I, \] that is, the sample covariance matrix of the history of the chain plus a (small) constant $\epsilon>0$ multiple of the identity matrix $I$. The lower bound on the eigenvalues of $S_n$ induced by the factor $\epsilon I$ is theoretically convenient, but practically cumbersome, as a good value for the parameter $\epsilon$ may not always be easy to choose. This article considers variants of the AM algorithm that do not explicitly bound the eigenvalues of $S_n$ away …

Statistics and ProbabilityFOS: Computer and information sciencesIdentity matrixMathematics - Statistics TheoryStatistics Theory (math.ST)Upper and lower boundsStatistics - Computation93E3593E15Combinatorics60J27Mathematics::ProbabilityLaw of large numbers65C40 60J27 93E15 93E35stochastic approximationFOS: MathematicsEigenvalues and eigenvectorsComputation (stat.CO)Metropolis algorithmMathematicsProbability (math.PR)Zero (complex analysis)CovariancestabilityUniform continuityBounded function65C40Statistics Probability and Uncertaintyadaptive Markov chain Monte CarloMathematics - Probability
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SPECTRAL ANALYSIS WITH TAPERED DATA

1983

. A new method based on an upper bound for spectral windows is presented for investigating the cumulants of time series statistics. Using this method two classical results are proved for tapered data. In particular, the asymptotic normality for a class of spectral estimates including estimates for the spectral function and the covariance function is proved under integrability conditions on the spectra using the method of cumulants.

Statistics and ProbabilityMathematical optimizationCovariance functionSeries (mathematics)Applied MathematicsAsymptotic distributionMaximum entropy spectral estimationUpper and lower boundsSpectral lineApplied mathematicsSpectral analysisStatistics Probability and UncertaintyCumulantMathematicsJournal of Time Series Analysis
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Minimax estimation with additional linear restrictions - a simulation study

1988

Let the parameter vector of the ordinary regression model be constrained by linear equations and in addition known to lie in a given ellipsoid. Provided the weight matrix A of the risk function has rank one, a restricted minimax estimator exists which combines both types of prior information. For general n.n.d. A two estimators as alternatives to the unfeasible exact minimax estimator are developed by minimizing an upper and a lower bound of the maximal risk instead. The simulation study compares the proposed estimators with competing least-squares estimators where remaining unknown parameters are replaced by suitable estimates.

Statistics and ProbabilityMathematical optimizationRank (linear algebra)Modeling and SimulationLinear regressionStatisticsEstimatorMinimax estimatorMinimaxEllipsoidUpper and lower boundsLinear equationMathematicsCommunications in Statistics - Simulation and Computation
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On an approximation problem for stochastic integrals where random time nets do not help

2006

Abstract Given a geometric Brownian motion S = ( S t ) t ∈ [ 0 , T ] and a Borel measurable function g : ( 0 , ∞ ) → R such that g ( S T ) ∈ L 2 , we approximate g ( S T ) - E g ( S T ) by ∑ i = 1 n v i - 1 ( S τ i - S τ i - 1 ) where 0 = τ 0 ⩽ ⋯ ⩽ τ n = T is an increasing sequence of stopping times and the v i - 1 are F τ i - 1 -measurable random variables such that E v i - 1 2 ( S τ i - S τ i - 1 ) 2 ∞ ( ( F t ) t ∈ [ 0 , T ] is the augmentation of the natural filtration of the underlying Brownian motion). In case that g is not almost surely linear, we show that one gets a lower bound for the L 2 -approximation rate of 1 / n if one optimizes over all nets consisting of n + 1 stopping time…

Statistics and ProbabilityRandom time netsMeasurable functionStochastic processStochastic integralsApplied MathematicsUpper and lower boundsNatural filtrationCombinatoricsModeling and SimulationStopping timeModelling and SimulationAlmost surelyApproximationBorel measureBrownian motionMathematicsStochastic Processes and their Applications
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On the gonality and the slope of a fibered surface

2018

Abstract Let f : X → B be a locally non-trivial relatively minimal fibration of curves of genus g ≥ 2 . We obtain a lower bound of the slope λ ( f ) increasing with the gonality of the general fiber of f. In particular, we show that λ ( f ) ≥ 4 provided that f is non-hyperelliptic and g ≥ 16 .

Surface (mathematics)General Mathematics010102 general mathematicsFibrationFibered knot01 natural sciencesUpper and lower boundsCombinatoricsGenus (mathematics)0103 physical sciences010307 mathematical physicsFiber0101 mathematicsMathematicsAdvances in Mathematics
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Learning small programs with additional information

1997

This paper was inspired by [FBW 94]. An arbitrary upper bound on the size of some program for the target function suffices for the learning of some program for this function. In [FBW 94] it was discovered that if “learning” is understood as “identification in the limit,” then in some programming languages it is possible to learn a program of size not exceeding the bound, while in some other programming languages this is not possible.

Theoretical computer sciencebusiness.industryComputer sciencemedia_common.quotation_subjectInductive reasoningMachine learningcomputer.software_genreUpper and lower boundsIdentification (information)Recursive functionsArtificial intelligenceLimit (mathematics)businessFunction (engineering)computermedia_common
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Descriptional and Computational Complexity of the Circuit Representation of Finite Automata

2018

In this paper we continue to investigate the complexity of the circuit representation of DFA—BC-complexity. We compare it with nondeterministic state complexity, obtain upper and lower bounds which differ only by a factor of 4 for a Binary input alphabet. Also we prove that many simple operations (determining if a state is reachable or if an automaton is minimal) are PSPACE-complete for DFA given in circuit representation.

TheoryofComputation_COMPUTATIONBYABSTRACTDEVICESFinite-state machineTheoretical computer scienceComputational complexity theoryComputer science020208 electrical & electronic engineering020206 networking & telecommunications02 engineering and technologyUpper and lower boundsAutomatonNondeterministic algorithmTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESSimple (abstract algebra)0202 electrical engineering electronic engineering information engineeringState (computer science)Representation (mathematics)Computer Science::Formal Languages and Automata Theory
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Upper bounds on multiparty communication complexity of shifts

1996

We consider some communication complexity problems which arise when proving lower bounds on the complexity of Boolean functions. In particular, we prove an \(O(\frac{n}{{2\sqrt {\log n} }}\log ^{1/4} n)\)upper bound on 3-party communication complexity of shifts, an O(n e ) upper bound on the multiparty communication complexity of shifts for a polylogarithmic number of parties. These bounds are all significant improvements over ones recently considered “unexpected” by Pudlak [5].

TheoryofComputation_MISCELLANEOUSDiscrete mathematicsCombinatoricsTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYCommunication complexityBinary logarithmBoolean functionUpper and lower boundsMultiparty communicationMathematics
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