Berry–Esseen bounds for multivariate nonlinear statistics with applications to M-estimators and stochastic gradient descent algorithms
Qi-Man Shao, Zhuo-Song Zhang
Abstract
We establish a Berry–Esseen bound for general multivariate nonlinear statistics by developing a new multivariate-type randomized concentration inequality. The bound is the best possible for many known statistics. As applications, Berry–Esseen bounds for M-estimators and averaged stochastic gradient descent algorithms are obtained.
Topics & Concepts
MathematicsMultivariate statisticsEstimatorStochastic gradient descentApplied mathematicsStatisticsNonlinear systemComputer sciencePhysicsMachine learningQuantum mechanicsArtificial neural networkStatistical Methods and InferenceRandom Matrices and ApplicationsMarkov Chains and Monte Carlo Methods