1
$\begingroup$

If a sequence of measurable mappings defined from a measure spaces to another measure space converges in different modes (see Wikipedia and John Cook's site), I wonder if there are some concepts capturing their rates of convergence for different modes of convergence?

You may restrict the discussion to probability theory. One example is in statistics. Suppose $\theta_n$ is an estimator for $\theta^*$ based on a sample with sample size $n$. I was wondering how the rate of convergence of $\theta_n$ is defined?

I also appreciate if there can be some references offered.

Thanks and regards!

  • 0
    [Modes of convergence](http://www.johndcook.com/modes_of_convergence.html)2012-02-16
  • 0
    Thanks! How about rate of convergence?2012-02-16

1 Answers 1