A sequence of univariate or multivariate independent random variables is considered and the problem of estimating their central moments and covariances, is examined. The estimators are based on previous observations and on the assumption that the quantities to be estimated follow unknown trends of a specified form. Convergence in quadratic mean is proved and the corresponding rate of convergence is evaluated. The results obtained are used in order to propose a dymanic method of moments for a time-dependent population.
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