Least Squares tail estimator
Computes the Least Squares (LS) estimates of the EVI based on the last k observations of the generalised QQ-plot.
LStail(data, rho = -1, lambda = 0.5, logk = FALSE, plot = FALSE, add = FALSE,
main = "LS estimates of the EVI", ...)
TSfraction(data, rho = -1, lambda = 0.5, logk = FALSE, plot = FALSE, add = FALSE,
main = "LS estimates of the EVI", ...)data |
Vector of n observations. |
rho |
Estimate for ρ, or |
lambda |
Parameter used in the method of Beirlant et al. (2002), only used when |
logk |
Logical indicating if the estimates are plotted as a function of \log(k) ( |
plot |
Logical indicating if the estimates of γ should be plotted as a function of k, default is |
add |
Logical indicating if the estimates of γ should be added to an existing plot, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
We estimate γ (EVI) and b using least squares on the following regression model (Beirlant et al., 2005): Z_j = γ + b(n/k) (j/k)^{-ρ} + ε_j with Z_j = (j+1) \log(UH_{j,n}/UH_{j+1,n}) and UH_{j,n}=X_{n-j,n}H_{j,n}, where H_{j,n} is the Hill estimator with threshold X_{n-j,n}.
See Section 5.8 of Beirlant et al. (2004) for more details.
The function TSfraction is included for compatibility with the old S-Plus code.
k |
Vector of the values of the tail parameter k. |
gamma |
Vector of the corresponding LS estimates for the EVI. |
b |
Vector of the corresponding LS estimates for b. |
rho |
Vector of the estimates for ρ when |
Tom Reynkens based on S-Plus code from Yuri Goegebeur.
Beirlant, J., Dierckx, G. and Guillou, A. (2005). "Estimation of the Extreme Value Index and Regression on Generalized Quantile Plots." Bernoulli, 11, 949–970.
Beirlant, J., Dierckx, G., Guillou, A. and Starica, C. (2002). "On Exponential Representations of Log-spacing of Extreme Order Statistics." Extremes, 5, 157–180.
Beirlant J., Goegebeur Y., Segers, J. and Teugels, J. (2004). Statistics of Extremes: Theory and Applications, Wiley Series in Probability, Wiley, Chichester.
data(soa) # LS tail estimator LStail(soa$size, plot=TRUE, ylim=c(0,0.5))
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