How to make a Hill Plot

By H. Drees, Laurens de Haan, Sidney I. Resnick. 2000

267 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e4aa873b4e101237a5dc5a7d3b5c6c5af817d500

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Citations in the corpus

A moving window approach for nonparametric estimation of the conditional tail index (2008, methodology): “See also [15] for approximations of the Hill process by sums of standard exponential random variables.”
Diverging Moments and Parameter Estimation (2005, methodology): “…as a generalpurpose tool to parametric estimators [see, e.g., the Hill estimator and its various improvements (Hill 1975; Kratz and Resnick 1995; Resnick, Dress, and Haan 1998; Bianchi and Meerschaert 2000), tail estimators (DuMouchel 1983; McCulloch 1997), and the comparative study conducted…”
Hidden regular variation and the rank transform (2005, background): “Diagnostic plots (not shown) such as the Hill, altHill, and quantile–quantile (QQ) plots (Beirlant et al. (1996), Drees et al. (2000), Kratz and Resnick (1996), Resnick (2003), Resnick and Stărică (1997)) suggest that k = 300 is appropriate for estimation of the marginal parameters α(1) and α(2).”
Measuring Tail Thickness under GARCH and an Application to Extreme Exchange Rate Changes (2003, methodology): “For the Drees et al. (2000) maximum occupation time estimator [Eq. (2.17)], the continuous parameter u is approximated by a grid with stepsize 0.05, where the upper bound u¯ =ln([T/2])/ln(T) corresponds to kV[T/2].”
Statistics of Extremes (2004, background): “A recommendable overview with numerous references of extreme value theory for heavy-tailed linear time series is Chapter 7 of Embrechts et al. (1997). Particularly popular in finance are the auto-regressive conditionally heteroscedastic (ARCH) process (Engle 1982) and its numerous ramifications, in ”
Modeling growth stocks via birth-death processes (2003, methodology): “An alternative way to estimate g/λ is to use the nonparametric Hill estimator or its extension such as the Hill ratio plot; see, for example, Hill (1975), Lo (1986), Embrechts et al. (1997), Adler et al. (1998), Drees et al. (2000).”
A Review of Extreme Value Threshold Estimation and Uncertainty Quantification (2012, methodology): “Drees et al. (2000) show that the 'altplot' of Resnick & Starica (1997), which is a simple modification to the Hill plot, by essentially using a log-scale on the k-axis, is beneficial for cases where the slowly varying function is non-constant but also state this is not a panacea for threshold…”
MULTI-FACTOR JUMP-DIFFUSION MODELS OF ELECTRICITY PRICES (2008, background): “This estimator is consistent under a broad set of assumptions (see [4] for a review).”