Empirical Process Techniques for Dependent Data

By Herold G. Dehling, W. Philipp. 2002

261 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3b1dc6bb7e8e01d24f736b2e050aa49b5d23bdb9

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Citations in the corpus

Asymptotic results for the empirical process of stationary sequences (2009, unknown): “[26]) obtain weak convergence to a Gaussian process.”
Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models (2006, methodology): “We also have the Glivenko–Cantelli theorem for stationary and ergodic sequences (see Dehling and Philipp 2002, p. 4).”
Sequential complexities and uniform martingale laws of large numbers (2015, background): “We refer the reader to [2, 10] for a more comprehensive survey of results for non-i.”
Threshold quantile autoregressive models (2011, unknown): “The hypothesis tests for the linearity of the quantile process are developed in Galvao et al. (2008). As in the regime switching and structural break literatures two different types of tests are studied, supremum and average Wald tests. For nonstandard cases given by an unknown threshold parameter t”
Random Forests for dependent data (2020, background): “However, existing ULLN results for α-mixing processes require the class of functions in Fn to be Lipschitz continuous [19].”
Empirical process results for exchangeable arrays (2019, methodology): “We refer to, e.g., van der Vaart and Wellner (1996) and Dehling and Philipp (2002) for overviews with respectively i.i.d. and time series data (see also, e.g., Bertail et al., 2017, for recent results on sampling designs).”
On the Bahadur representation of sample quantiles for dependent sequences (2005, background): “Further references on this topic can be found in the recent survey edited by Dehling, Mikosch and Sorensen [6].”
Recent advances in invariance principles for stationary sequences (2006, background): “For processes with short memory the theory of the weak invariance principle is very well fine tuned under various mixing conditions (see, e.g. the surveys by Peligrad [47], Philipp [58], Rio [61], Dehling and Philipp [14], and books by Bradley [5, 6]).”
Model Checks Using Residual Marked Empirical Processes (2004, background): “Dehling and Philipp (2002, p. 4) , and Wolfowitz (1954), the uniform convergence holds for 1(It�1 � x) and 1(� � It�1 � u), respectively.”
TFT-bootstrap: Resampling time series in the frequency domain to obtain replicates in the time domain (2011, unknown): “The Annals of Statistics 2011, Vol. 39, No. 3, 1427–1470 DOI: 10.1214/10-AOS868 © Institute of Mathematical Statistics, 2011”
Inference on Directionally Differentiable Functions (2014, background): “Primitive conditions for the functional central limit theorem to hold can be found, for example, in Dehling and Philipp (2002).”