Abstract
Abstract It is well known that the sample mean, based on a sequence of independent random variables with common distribution, is a weakly consistent estimator as well as a strongly consistent estimator for the population mean. The first property is the famous weak law of large numbers (Khinchin), the second property is the strong law of large numbers (Kolmogorov). Both laws are key results of modern probability theory. Similar properties hold for more complicated sequences of random variables, for example, for sequences satisfying the stationarity assumption or for martingale sequences. These extensions are of crucial importance for statistical applications in ergodic theory and survival analysis.
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