Search results for "Robbins-Monro"

showing 1 items of 1 documents

Recursive estimation of the conditional geometric median in Hilbert spaces

2012

International audience; A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirm…

Statistics and ProbabilityMallows-Wasserstein distanceRobbins-Monroasymptotic normalityCLTcentral limit theoremAsymptotic distributionMathematics - Statistics TheoryStatistics Theory (math.ST)01 natural sciencesMallows–Wasserstein distanceonline data010104 statistics & probability[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]60F05FOS: MathematicsApplied mathematics[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]0101 mathematics62L20MathematicsaveragingSequential estimation010102 general mathematicsEstimatorRobbins–MonroConditional probability distribution[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]Geometric medianstochastic gradient[ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH]robust estimatorRate of convergenceConvergence of random variablesStochastic gradient.kernel regressionsequential estimationKernel regressionStatistics Probability and Uncertainty
researchProduct