Doukhan, Paul; Prohl, Silika; Robert, Christian Y. Subsampling weakly dependent time series and application to extremes. (English) Zbl 1274.62586 Test 20, No. 3, 447-479 (2011). Summary: This paper provides extensions of the work on subsampling by P. Bertail et al. [J. Econom. 120, No. 2, 295–326 (2004; Zbl 1282.62188)] for strongly mixing case to weakly dependent case by application of the results of P. Doukhan and S. Louhichi [Stochastic Processes Appl. 84, No. 2, 313–342 (1999; Zbl 0996.60020)]. We investigate properties of smooth and rough subsampling estimators for sampling distributions of converging and extreme statistics when the underlying time series is \(\eta\)- or \(\lambda\)-weakly dependent. Cited in 6 ReviewsCited in 3 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G30 Order statistics; empirical distribution functions 62G32 Statistics of extreme values; tail inference Keywords:subsampling; weakly dependent time series; max-stable distributions Citations:Zbl 0996.60020; Zbl 1282.62188 PDFBibTeX XMLCite \textit{P. Doukhan} et al., Test 20, No. 3, 447--479 (2011; Zbl 1274.62586) Full Text: DOI arXiv References: [1] Andersson CW (1970) Extreme value theory for a class of discrete distributions with applications to some stochastic processes. J Appl Probab 7:99–113 · Zbl 0192.54202 [2] Andrews D (1984) Non strong mixing autoregressive processes. J Appl Probab 21:930–934 · Zbl 0552.60049 [3] Ango Nze P, Doukhan P (2004) Weak dependence and applications to econometrics. Econom Theory 20:995–1045 · Zbl 1069.62070 [4] Bertail P, Haefke C, Politis DN, White W (2004) Subsampling the distribution of diverging statistics with applications to finance. J Econom 120:295–326 · Zbl 1282.62188 [5] Bickel P, Götze F, van Zwet W (1997) Resampling fewer than n observations: gains, losses and remedies for losses. Stat Sin 7:1–31 · Zbl 0927.62043 [6] Carlstein E (1986) The use of subseries values for estimating the variance of a general statistic from a stationary time series. Ann Stat 14:1171–1179 · Zbl 0602.62029 [7] Chernick M (1981) A limit theorem for the maximum of autoregressive processes with uniform marginal distribution. Ann Probab 9:145–149 · Zbl 0453.60026 [8] Dedecker J, Doukhan P, Lang G, León JR, Louhichi S, Prieur C (2007) Weak dependence: Models, theory and applications. Lecture notes in statistics, vol 190. Springer, New York · Zbl 1165.62001 [9] Doukhan P (1994) Mixing: properties and examples. Lecture notes in statistics, vol 85. Springer, New York · Zbl 0801.60027 [10] Doukhan P, Latour A, Oraichi D (2006) A simple integer-valued bilinear time series model. Adv Appl Probab 38:559–578 · Zbl 1096.62082 [11] Doukhan P, Louhichi S (1999) A new weak dependence condition and applications to moment inequalities. Stoch Process Appl 84:313–342 · Zbl 0996.60020 [12] Doukhan P, Mayo N, Truquet L (2009) Weak dependence, models and some applications. Metrika 69(2–3):199–225 · Zbl 1433.60017 [13] Doukhan P, Teyssière G, Winant P (2006) A LARCH( vector valued process. Dependence in probability and statistics. Lecture notes in statist, vol 187. Springer, New York, pp. 245–258. · Zbl 1113.60038 [14] Doukhan P, Wintenberger O (2007) An invariance principle for weakly dependent stationary general models. Probab Math Stat 27:45–73 · Zbl 1124.60031 [15] Doukhan P, Wintenberger O (2008) Weakly dependent chains with infinite memory. Stoch Process Appl 118:1997–2013 · Zbl 1166.60031 [16] Hall A, Scotto MG, Cruz J (2010) Extremes of integer-valued moving average sequences. Test 19:359–374 · Zbl 1203.60056 [17] Künsch HR (1989) The jackknife and the bootstrap for general stationary observations. Ann Stat 17:1217–1241 · Zbl 0684.62035 [18] Leadbetter MR (1974) On extreme values in stationary sequences. Z Wahrscheinlichkeitstheor Verw Geb 28:289–303 · Zbl 0265.60019 [19] Leadbetter MR, Lindgren G, Rootzen H (1983) Extremes and related properties of random sequences and processes. Springer series in statistics · Zbl 0518.60021 [20] Nordman DJ, Lahiri SN (2004) On optimal spatial subsample size for variance estimation. Ann Stat 32:1981–2027 · Zbl 1056.62055 [21] O’Brien GL (1987) Extreme values for stationary and Markov sequences. Ann Probab 15:281–291 · Zbl 0619.60025 [22] Politis DN, Romano JP (1994) Large sample confidence regions based on subsamples under minimal assumptions. Ann Stat 22:2031–2050 · Zbl 0828.62044 [23] Robert C, Segers J, Ferro C (2009) A sliding blocks estimator for the extremal index. Electron J Stat 3:993–1020 · Zbl 1326.60075 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.