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Extra info for Spectral Analysis and Time Series. Volume 1: Univariate Series.

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3 in Bertail & Cl´emen¸con (2004c)), Theorem 3. 1 . Remark 5. The condition αn = o(n−1/2 ) as n → ∞ may be ensured by smoothness conditions satisfied by the transition kernel p(x, y): under H¨ older constraints of order s such rates are achieved as soon as s > 1, that is a rather weak assumption. , studentized ) sample mean by ςn = n1/2 σ −1 (f )(µn (f ) − µ(f )) , tn = n1/2 σn (f )−1 (µn (f ) − µ(f )) . A M The following theorem straightforwardly results from Theorem 3. Regeneration-based statistics for Harris recurrent Markov chains 25 Theorem 4.

Sigman, K. (1992). Work-modulated queues with applications to storage processes. J. Appl. , 29, 699-712. [B¨ ul97] B¨ uhlmann, P. (1997). Sieve Bootstrap for time series. Bernoulli, 3, 123-148. [B¨ ul02] B¨ uhlmann, P. (2002). Bootstrap for time series. Stat. , 17, 52-72. , Veraverbeke, N. (1981). The order of the normal approximation for a Studentized statistic. Ann. , 9, 194-200. [Car86] Carlstein, E. (1986). The use of subseries values for estimating the variance of a general statistic from a stationary sequence.

This can be done by adapting standard SLLN arguments for U -statistics. 7 Robust functional parameter estimation Extending the notion of influence function and/or robustness to the framework of general time series is a difficult task (see K¨ unsch (1984) or Martin & Yohai (1986)). Such concepts are important not only to detect ”outliers” among the data or influential observations but also to generalize the important notion of efficient estimation in semiparametric frameworks (see the recent discussion in Bickel & Kwon (2001) for instance).

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