Continuous mapping approach to the asymptotics of $U$- and $V$-statistics

[12] Denker, M. (1985). <i>Asymptotic Distribution Theory in Nonparametric Statistics. Advanced Lectures in Mathematics</i>. Braunschweig: Friedr. Vieweg &amp; Sohn.

[13] Ghorpade, S.R. and Limaye, B.V. (2010). <i>A Course in Multivariable Calculus and Analysis. Undergraduate Texts in Mathematics</i>. New York: Springer.

[26] Pollard, D. (1984). <i>Convergence of Stochastic Processes. Springer Series in Statistics</i>. New York: Springer.

[28] Serfling, R.J. (1980). <i>Approximation Theorems of Mathematical Statistics</i>. New York: Wiley.

[30] Shorack, G.R. and Wellner, J.A. (1986). <i>Empirical Processes with Applications to Statistics. Wiley Series in Probability and Mathematical Statistics</i>: <i>Probability and Mathematical Statistics</i>. New York: Wiley.

[38] Zähle, H. (2014). Marcinkiewicz-Zygmund and ordinary strong laws for empirical distribution functions and plug-in estimators. <i>Statistics</i>. To appear.

[31] van der Vaart, A.W. (1998). <i>Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics</i> <b>3</b>. Cambridge: Cambridge Univ. Press.

[1] Andersen, N.T., Giné, E. and Zinn, J. (1988). The central limit theorem for empirical processes under local conditions: The case of Radon infinitely divisible limits without Gaussian component. <i>Trans. Amer. Math. Soc.</i> <b>308</b> 603–635.

[2] Arcones, M.A. and Giné, E. (1992). On the bootstrap of $U$ and $V$ statistics. <i>Ann. Statist.</i> <b>20</b> 655–674.

[3] Avram, F. and Taqqu, M.S. (1987). Noncentral limit theorems and Appell polynomials. <i>Ann. Probab.</i> <b>15</b> 767–775.

[4] Beutner, E., Wu, W.B. and Zähle, H. (2012). Asymptotics for statistical functionals of long-memory sequences. <i>Stochastic Process. Appl.</i> <b>122</b> 910–929.

[5] Beutner, E. and Zähle, H. (2010). A modified functional delta method and its application to the estimation of risk functionals. <i>J. Multivariate Anal.</i> <b>101</b> 2452–2463.

[6] Beutner, E. and Zähle, H. (2012). Deriving the asymptotic distribution of U- and V-statistics of dependent data using weighted empirical processes. <i>Bernoulli</i> <b>18</b> 803–822.

[7] Beutner, E. and Zähle, H. (2014). Supplement to “Continuous mapping approach to the asymptotics of $U$- and $V$-statistics.” <a href="DOI:10.3150/13-BEJ508SUPP">DOI:10.3150/13-BEJ508SUPP</a>.

[8] Chen, X. and Fan, Y. (2006). Estimation of copula-based semiparametric time series models. <i>J. Econometrics</i> <b>130</b> 307–335.

[9] Dehling, H. (2006). Limit theorems for dependent $U$-statistics. In <i>Dependence in Probability and Statistics. Lecture Notes in Statist.</i> <b>187</b> 65–86. New York: Springer.

[10] Dehling, H. and Taqqu, M.S. (1989). The empirical process of some long-range dependent sequences with an application to $U$-statistics. <i>Ann. Statist.</i> <b>17</b> 1767–1783.

[11] Dehling, H. and Taqqu, M.S. (1991). Bivariate symmetric statistics of long-range dependent observations. <i>J. Statist. Plann. Inference</i> <b>28</b> 153–165.

[14] Gill, R.D., van der Laan, M.J. and Wellner, J.A. (1995). Inefficient estimators of the bivariate survival function for three models. <i>Ann. Inst. Henri Poincaré Probab. Stat.</i> <b>31</b> 545–597.

[15] Giraitis, L. and Surgailis, D. (1999). Central limit theorem for the empirical process of a linear sequence with long memory. <i>J. Statist. Plann. Inference</i> <b>80</b> 81–93.

[16] Halmos, P.R. (1946). The theory of unbiased estimation. <i>Ann. Math. Statist.</i> <b>17</b> 34–43.

[17] Ho, H.C. and Hsing, T. (1996). On the asymptotic expansion of the empirical process of long-memory moving averages. <i>Ann. Statist.</i> <b>24</b> 992–1024.

[18] Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution. <i>Ann. Math. Statist.</i> <b>19</b> 293–325.

[19] Hosking, J.R.M. (1981). Fractional differencing. <i>Biometrika</i> <b>68</b> 165–176.

[20] Hsing, T. (2000). Linear processes, long-range dependence and asymptotic expansions. <i>Stat. Inference Stoch. Process.</i> <b>3</b> 19–29.

[21] Koroljuk, V.S. and Borovskich, Y.V. (1994). <i>Theory of $U$-statistics. Mathematics and Its Applications</i> <b>273</b>. Dordrecht: Kluwer Academic.

[22] Lee, A.J. (1990). <i>$U$-Statistics</i>: <i>Theory and Practice. Statistics</i>: <i>Textbooks and Monographs</i> <b>110</b>. New York: Dekker.

[23] Lévy-Leduc, C., Boistard, H., Moulines, E., Taqqu, M.S. and Reisen, V.A. (2011). Asymptotic properties of $U$-processes under long-range dependence. <i>Ann. Statist.</i> <b>39</b> 1399–1426.

[24] Lévy-Leduc, C., Boistard, H., Moulines, E., Taqqu, M.S. and Reisen, V.A. (2011). Large sample behaviour of some well-known robust estimators under long-range dependence. <i>Statistics</i> <b>45</b> 59–71.

[25] Mattila, P. (1995). <i>Geometry of Sets and Measures in Euclidean Spaces</i>: <i>Fractals and Rectifiability. Cambridge Studies in Advanced Mathematics</i> <b>44</b>. Cambridge: Cambridge Univ. Press.

[27] Rio, E. (1995). A maximal inequality and dependent Marcinkiewicz–Zygmund strong laws. <i>Ann. Probab.</i> <b>23</b> 918–937.

[29] Shao, Q.M. and Yu, H. (1996). Weak convergence for weighted empirical processes of dependent sequences. <i>Ann. Probab.</i> <b>24</b> 2098–2127.

[32] Veillette, M.S. and Taqqu, M.S. (2013). Properties and numerical evaluation of the Rosenblatt distribution. <i>Bernoulli</i> <b>19</b> 982–1005.

[33] von Mises, R. (1947). On the asymptotic distribution of differentiable statistical functions. <i>Ann. Math. Statist.</i> <b>18</b> 309–348.

[34] Wu, W.B. (2003). Empirical processes of long-memory sequences. <i>Bernoulli</i> <b>9</b> 809–831.

[35] Wu, W.B. (2006). Unit root testing for functionals of linear processes. <i>Econometric Theory</i> <b>22</b> 1–14.

[36] Wu, W.B. (2008). Empirical processes of stationary sequences. <i>Statist. Sinica</i> <b>18</b> 313–333.

[37] Yukich, J.E. (1992). Weak convergence of smoothed empirical processes. <i>Scand. J. Stat.</i> <b>19</b> 271–279.