Before proving the central limit theorems, we will spend a lot efforts in studying the second moments, which enable us to reduce the infinite Fourier series in Theorems 3 and 4 to finite sums, and hence we can apply the moment inequalities stated in…
In this section we provide the statements of our main results. Complete proofs can be found in , where these results have originally appeared.
We would like to thank Professor Peter Rousseeuw for carefully reading the first draft and for pointing us to a proof of an upper bound for the breakdown point.
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