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About:Stochastic equicontinuity

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In estimation theory in statistics, stochastic equicontinuity is a property of estimators (estimation procedures) that is useful in dealing with their asymptotic behaviour as the amount of data increases. It is a version of equicontinuity used in the context of functions of random variables: that is, random functions. The property relates to the rate of convergence of sequences of random variables and requires that this rate is essentially the same within a region of the parameter space being considered.

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  • In estimation theory in statistics, stochastic equicontinuity is a property of estimators (estimation procedures) that is useful in dealing with their asymptotic behaviour as the amount of data increases. It is a version of equicontinuity used in the context of functions of random variables: that is, random functions. The property relates to the rate of convergence of sequences of random variables and requires that this rate is essentially the same within a region of the parameter space being considered. For instance, stochastic equicontinuity, along with other conditions, can be used to show uniform weak convergence, which can be used to prove the convergence of extremum estimators. (en)
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  • In estimation theory in statistics, stochastic equicontinuity is a property of estimators (estimation procedures) that is useful in dealing with their asymptotic behaviour as the amount of data increases. It is a version of equicontinuity used in the context of functions of random variables: that is, random functions. The property relates to the rate of convergence of sequences of random variables and requires that this rate is essentially the same within a region of the parameter space being considered. (en)
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  • Stochastic equicontinuity (en)
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